Ser Arlan, and eventually Dunk, both believed Baelor Targaryen was "the heart of chivalry and the soul of wisdom", and at the end of the day, they were right. The only thing is, they had no idea what it is like to be a nobleman. Especially a prince and heir to the Iron Throne. Especially the first half Targaryen, half Martell prince ever. Especially the prince who had fought in a civil war against certain members of his own family about a decade earlier. And the list goes on.
Dunk's point of view and the way he sees Baelor is a beautiful simplification for the sake of the story, but can be dangerous in the sense that it can lead to oversimplifications and black-and-white thinking. Like, Baelor could do no wrong, or Maekar was a villain, or Baelor cared about Dunk only, etc., etc. It can be far too easy to ignore the reality of Baelor being a good, but complicated man, whose judgment was not always perfect. They are only human, and they are flawed, just like everyone else, and this is sort of the point here as well.
I like the idea that no one is pure goodness, just like no one is pure evil, even though this, too, can be a slippery slope in terms of the extent and the good old moral ambiguity. Namely, what, exactly, are the lengths that this good man can go to, when he feels he has to, or simply wants to? In Baelor's case, this question remains largely unanswered.
The thing is (I believe) that this whole affair was not just about "Dunk and Baelor's goodness versus Aerion's wickedness". It was also "a small man versus the royals", "the royals versus public opinion", and "the royals versus gods". There were so many ways this could go catastrophically wrong for the Targaryens, and Baelor was trying to prevent that by putting himself on the line, as the man who held most of the power and responsibility. And of course he could have used his power in so many other ways. He could have put Dunk back in prison and taken his time. He could have put Aerion and Daeron in prison as well, if they still insisted on their games involving "high treason". He could have found, or appointed, or hired a fighter, or two, or three for Dunk, and then he could have sat back and watched the show.
However, the fighters turn up themselves (thanks to Aegon and the fact that Aerion has an impressive ability to make enemies). But Steffon Fossoway gets bought to Aerion's side, and by this point the game has become so rigged it's unbelievable. And Baelor, as a Targaryen prince, a nobleman in the best sense of the word, a man of honor, and one of the best fighters in the realm, cannot remain neutral, because he cares for the truth. "Goodness is as goodness does", as we know. I believe he is capable of deep empathy, just like Dunk, who seems to empathize with every living creature he encounters. And on top of it all, he can see the injustice being done to Dunk by the Targaryens more clearly than anyone else, what with the trial of seven being basically a trap, and the alternative for Dunk being essentially a slow death, had they actually chopped off his hand and his foot. But the fact that Baelor had to ride into the arena at all should give you an idea of just how dire the situation was. Publicly. Politically. Personally. It was awful both for Baelor and for Maekar.
In fact, Baelor was so desperate to fix the situation (while making it much, much worse within his own family, though), that he actually went into a serious fight without being armored up properly. He wasn't wearing a proper helmet, of all things, which is an incredibly reckless thing to do, if you think about it, no matter how experienced, perhaps, even practically unbeatable you are as a fighter. It's just something you're strongly advised not to do, no matter how confident you feel.
And he knew exactly what he was doing, and to what extent his son's armor didn't fit him. The grand toss of his head when he takes off the helmet in front of Dunk and the crowd is because the helmet is too tight. All it essentially did was give him, and others as well, a false sense of security. And I'd love to see if Maekar had tried to pull off something like this, especially in their younger years. Baelor would have told him — absolutely not, you are not doing this, and only over my dead body, I imagine. But this, of course, was different.
I could also go on a tangent about the "how dare he love his flawed brother, when he's so perfect" thing. Well, maybe it's because they are brothers? And neither is perfect? And the love was earned? You can say what you want about the brothers' relationship and their traits. But saying that Baelor's love for Maekar, which he displayed literally until his final moments, was hollow and meaningless, a "delusion", or maybe even an "act" (especially when there was literally no reason for him to put up an act in front of Fossoway), is an insult to Baelor's obvious intelligence. It essentially destroys Baelor's character — which some people, somehow, seem to believe they are uplifting by degrading Maekar. Any relationship that is not superficial is complicated, and we are talking about insanely complicated men, circumstances and lives here.
But let's just say they grew up, and learned, and made mistakes, and laughed, and cried, and loved, and hated, and fought together. They were the two warriors of their family, so they were bonded from a young age, they were naturally close, especially in their younger years. There was a strong bond there, and while a lot of different things can be said about its nature, its presence is undeniable, I think. In George R. R. Martin's works it goes to curious lengths — they even die in a similar manner. You don't even have to look for certain symbolism and an intricate, painfully pronounced connection here, because it was there in the first place.
And maybe, just maybe (most probably, actually), Baelor had also held the little, innocent Aerion in his arms and he remembered it, even while looking at the monster that Aerion finally became. And even more than that. If Baelor played a more or less constant, integral part in the life of Maekar's family — and apparently, he did — then, at least to a degree, Aerion is his creation as well. I mean, Baelor trained him, shouted at him, humiliated him and encouraged him in the yard just like Maekar did? You bet. Taught Aerion a trick or two that he would later use on Dunk, because Uncle Baelor had taught him what to do if things got nasty indeed? Absolutely. An ultimate Baelor-ish thing to do, if you ask me, when it comes to his sons or nephews.
And could Baelor have — inadvertently — planted in Aerion the idea that you can do whatever you want, if you're a Targaryen prince, as long as you stay, or at least pretend to stay within certain boundaries, which, again, are rather vague, because you're a Targaryen prince? I really don't know. Perhaps? But if there was one person within Baelor and Maekar's inner circle who could have guessed and believed that there was more to his father and uncle's past than they were letting on, and collected all the possible information and gossip on the subject — I bet you anything, it would be Aerion. (This is a fanon-ish tangent, but I just think it weaves into the story quite nicely.)
And he was comfortable as hell in Baelor’s presence literally until the very end, which tells you a lot not only about his impertinent nature, but also about the family dynamics there. Still, nobody is born a villain and nobody becomes a villain or a selfish monster overnight. It had to be a long process and it took years (as Daeron later pointed out to Dunk). So Baelor and Aerion were simply used to each other, just like everyone else in the family.
And another curious thing about Baelor and Aerion. "Aerion is your brother. And the septons say we must love our brothers" — excuse me, but you don't talk like this about someone you believe is completely irredeemable, you just don't. Even if it's your nephew whom you've known since birth and probably even helped raise to a degree — and still, most likely, you cannot know everything about him, simply because he's not your own son and your brother's family will obviously have its own boundaries — and secrets — regardless of how close you are, it's only natural. But this very well may also have something to do with "anger not being his default" (as Bertie Carvel put it). He is, obviously, terribly angry with Aerion at the moment, and disgusted by his actions — he might have even wanted to kick Aerion himself — but it looks like if they were not at Ashford, it would be just another damn evening in the Targaryen household. The main problem being — they are not at home, and they are under the scrutiny of commoners and nobles alike.
But back to Baelor — I don't think all of this affected his decisions, at least on the conscious level. He had to keep at least some semblance of peace between himself and Maekar, who sided with Aerion — as long as it was still possible, and even while deeply disagreeing with Maekar. He couldn't afford any further damage to their public image in any form. (Lord Leo Tyrell was also sitting there, by the way, representing the high nobility and hanging on every word.) And he wouldn't position himself or any of his relatives above the law. But still, it was his family. And let's not forget about Aegon, who can still turn out to be either good Aegon, or bad Aegon, and is watching things unravel. So Baelor feels obliged to set a good example.
A Knight of the Seven Kingdoms is also about legacy, among other things. And here it's not just in the noble deed itself, it's in the immense guilt and regret of those left behind, when this very deed turns out to be the one that kills Baelor. The gods are unknown, fates are cruel, good men make mistakes and die, no matter how wise or brave. The best you can do is to pass on the values you believed in, even if everything else fails. Baelor believed in justice and in chivalry. We cannot know what might have been had he lived, but at the very least, Aegon lives on. Aegon remembers. And Aegon becomes a good king.