Honestly,I think one of the reasons I hate how quickly the writing in TLO onward dropped mentioning Michael so fast is, not only cause I think he's a really interesting character and I love the Lil guy, but-
It's very likely that without his quick thinking, Kronos mightve won.
That, theoretically he dies before he can point out the fault in the bridge to Percy, maybe he's one of the demigods that Kronos knocks off earlier in the battle or something.
Percy is too focused on his fight with Kronos to notice the fault of have the same plan that Michael had, even more so with Annabeth being hurt and Michael being dead his fighting with a lot of grief and rage at that point (I mean, if he screams so loud it carried off into the air after he can't find Michael in canon, I imagine seeing him knocked off by Kronos along side Annabeth being hurt as well is gonna have him pretty upset.)
But at that point he's fighting mostly on his own, even if the living members of the Apollo cabin jump back in to help they're still highly outnumbered.
Percy might be mostly invincible with the Achilles curse, but it doesn't give him infinite energy. And not only is he fighting Kronos, but if Kronos told his army to back him up again they very much will. And 1 on gods know how many monsters and demigods ain't gonna do good
Especially since I'm sure Kronos is fully aware that Percy is gonna to avoid killing demigods as much as possible. And Kronos is willing to kill his own demigods so he's not holding anything back.
Maybe Percy's grief and rage might get him to be a tiny more reckless, but it's just a very bad situation if he doesn't notice the fault or manage to break the bridge in time.
Now if Kronos manages to wear Percy down enough to overwhelm him or whatever, idk exactly what he do after that? Find a way to keep him contained or attack every spot until he finds his weak point(like tigerclaw telling bluestar he'd keep killing her until all 9 lives were gone.) And we already know he had some close idea of where his weak spot was after Annabeth jumped in front of the knife sooo-
Anyway, yeah- so if both Michael and Percy are taken out the picture in the first battle, and Kronos marches on, there's multiple things that's gonna probably ensure his win.
1. He's likely gonna wipe out the rest of the Apollo cabin once he deals with Percy, which includes Will, and 11-12 year old Kayla and Austin(I'm mentioning their age mainly cause MY GODS THEY WERE BABIES)
2.Without an Apollo kid to heal Annabeth, I'm pretty sure it's heavily implied she wouldn't have made it. Like the Hunter's healing would not been enough. So they're out Annabeth too
3. The party ponies don't come until after Hyperion and all that iirc(like the end of the second night i think?) So there's no saving from them unless Chiron manages to convince them earlier but I'm running on the idea that it happens about the same as in canon with the Party Ponies.
4. Ares cabin doesn't come until the final day in canon. Now with this maybe Silena is able to report that Percy, Annabeth (if she dies before Silena goes to get the Ares cabin, at least she able to say Annabeth not looking good.),Michael, and the whole Apollo cabin been wiped out, and that might knock some sense into Clarisse to get her going earlier. But even then if Clarisse doesn't manage to get blessing of Ares somehow or whatever, they still might be cooked on that end in some form.
5. Hades, Persephone and Demeter probably wouldn't have made it in time either, maybe if Nico gets even more pushy after sensing Percy's death they might, but it's really up in the air how that'll work out and what would happen if they did get there earlier.
6. Poseidon is still focused on his fight in Atlantis, and without Percy he probably would jump in to take out Typhon. Maybe he might somehow go full rage of he manages to sense/ learn of Percy's death, but that's up in the air and, Like with 5, no telling how exactly that'll play out.
7. Gods likely will keep fighting Typhon. Which if the demigods and nature spirits are wiped out then Kronos going really have more freedom to tear down the thrones and wreck Olympus.
8. Rachel is a wild card, like maybe if she senses Percy might die at the bridge she might try to get to Manhattan before the battle even starts. But there's a lot of uncertainty if she could get there in time and everything. So that's up in the air at least
Over all, the BoM was 3 days of very close calls. The fact that the managed to push through each time by the hair of their chin is incredible and was built on a lot of lucky events.
Like a tower of cards. Remove one card the whole tower goes down.
And Michael's sacrifice was one of the cards that definitely kept Kronos from winning. And the fact that Rick doesn't even bother to finish his arc (We don't see Clarisse reaction to his death nor do we learn if his body was found or not, not even a burial shroud described, the chariot situation was solved off screen and then completely destroyed the next book. Like Rick did not give a care in the world about Michael after the bridge dhdyd)
It's very much a frustrating thing to me because how much Michael's death could've been something that really drove Percy in battle at least in one of the battles after Williamsburg Bridge. Heck, not only him connecting Ethan to Annabeth getting hurt but with Michael's death because he was there(even if he had nothing to do with it, Percy's at least gonna be frustrated with grief.)
The scene after Percy breaks the bridge is one of my favorites, because the small details. Kronos still looking a bit smug when he retreats. Percy's frantic search when he sees Michael's missing, HES SCREAM CARRYING INTO THE MORNING.
THE FACT MICHAEL DIES AS THE SUNS COMES UP,THAT HIS FINAL MOMENTS HE STILL GETS TO BE UNDER HIS FATHER'S LIGHT. THAT WILL RISES TO HIS POSITION AT DAWN-
And just. Michael Yew my beloved.