Personally, I don’t objectively mind picturing one of the Bats specifically Tim or Jason as Batman.
I do not honestly think being Batman is going to fundamentally kill something in them.
Dick and Damian are a different story because we’ve seen Dick as Batman, it fucks him up. Damian I enjoy that boy getting peace after spending his entire life fighting. 
Whenever I see arguments about how none of them can ever be Batman or comparison between them and Batman that are very negative.
The underline is many people just do not like Bruce.
Tim loves Bruce.
Jason could love Bruce again.
The Batman mantle is not this evil demented suit that will destroy everything about you.
Now in my own head, I don’t picture Tim as Batman but that’s because I’m making his daughter Batman. :)
Jason, would be an amazing Batman with the right writers and good motivations.
But in fandom land either Tim or Jason as Batman is not a warcrime. 
while i think Cassandra Cain would be the most suited batkid to become the next Batman, i don’t think Bruce would want any of them to take up the mantle. or at least, i don’t think he should want any of them to become the next Batman. especially after Dick took up the mantle while he was lost in the time stream.
he wouldn’t want to put that kind of pressure on them. Batman is more of a symbol than a name at this point, a moral compass that so many people look up to. he’s also deeply aware of his flaws and mistakes and he knows full well that most of them (bar maybe Cass i guess) have complicated feelings towards Batman.
he wasn’t fair to Dick while grieving Jason, and after, again, the time stream incident thing, Dick probably wouldn’t want to touch the cowl with a ten feet pole. if he’s wearing it it’s because he feels like he has to or he was pressured into it and that kind of mental prison is not something Bruce would want to inflict on his son.
for Jason, Batman is the man who chose a failing system over his broken son. there’s no doubt a lot of feelings of inadequacy and mistrust in there. it’s like all his insecurities taking shape to remind him he’s the black sheep. Jason would probably destroy Batman, if only to destroy the thing that gets in the way of his relationship with his dad. Bruce handing the cowl to Jason would be, in my humble opinion, akin to torture, and he would probably immolate himself before doing that.
to Tim, Batman is many things. not quite a mentor, not quite a boss, not quite a coworker, not quite a dad, not quite a friend. to him, Batman contains multiple. it comes with his overly analytic mind. but his relationship to Batman, as Tim, as Robin, as Red Robin, is transactional. it’s a business transaction. to keep Gotham safe, to keep Bruce alive. he doesn’t get anything from it but more responsibilities and more pressure and more stress and more work, and that’s without even touching the whole shitshow that was his sixteenth birthday. Bruce giving Batman to Tim would be like reducing him to what he can do. he’s a toolkit with infinite faces. they would lose Tim through the mantle. and Bruce wouldn’t do that.
for Damian, Batman is all he ever aspired to be. to give it to him would be a confirmation of his grandfather’s teachings and his predisposition for violence and blood. Bruce would avoid giving him the mantle at any cost, just so that he could be allowed to develop his own identity, and the fact that DC seems to be heading towards making him retire from the vigilante lifestyle to go to med school is amazing. that’s what his character needs. let him leave.
and now Cass. i’ve been thinking about her while writing the other entries, and honestly? she shouldn’t inherit the Batman mantle either. i know i’m contradicting myself but hear me out; Cassandra was brought up as a weapon, with the sole purpose of following orders and delivering kills. Batman and his mission allowed her to leave it all behind and find a new purpose, which is admirable, but that’s all it did. it redirected her and her training and her violence. she’s still doing the very same thing, with a different goal in mind and a looser leash. she’s still what her father made her to be, but with a different target and different guidelines. that’s not better. it’s not, in my opinion, a satisfying resolution to her character. so no, she shouldn’t be Batman. she could keep Orphan, but like Damian i think she could benefit from stepping away from that life all together.
I hate that DC keeps attempting to shroud in mystery who is going to be the next Batman when literally every single time the future has been shown since Damians been a thing the next Batman has been Damian 🙄
Like, I don't like it but obviously DC is going to favor Damian, they have since he's been around. He's the writer's pet. Not to mention the blood son "Son of the bat" bullshit
I feel like a lot of people view batman as a mantle and having a new batman, like shown in batman: beyond, but I think about it like a starting place. He shaped their morals every if they have changed a bit but he shaped their fighting style, they way that they handle cases and civilians. You know who has been trained by batman.
I'm just rambling now :3 but anyway
I just think that instead of passing on batman they should all train their own robins (probably not called that tho) as they change and grow, keeping the tradition so that Gotham never has a shortage of bats, birds, and other cryptids to keep them safe. Of course they should try and find their own city's but Gotham is always open to them.