As
Ishida loves to remind us the timey wimey shenanigans by the end of Cross almost certainly undo the deaths of the Trigger heroes (if nothing else Robo and Lucca are definitely still alive and for all we know the fall of Guardia at the hands of Porre was also part of Belthasar's plan), but I get it.
I banged on last page about the nature of stories, that fiction, even interconnected fiction, doesn't exist in a universe with its own rules, rather they are stories made at a specific point in time to impart a message. Chrono Cross would not be Chrono Cross if it didn't look at Chrono Trigger and ask "but what if this didn't work out?" and could really only exist in that specific context, because that was what Masato Kato wanted to impart. If he rewrote the story so that Crono and friends were alive and things worked out, there wouldn't be a Chrono Cross.
NeonZ put it well that, for all that Cross posits about the doomed journey of Crono, the game itself doesn't really put much effort into explaining why this one band of plucky adventurers crossed time and ruined everyone's day, but this subsequent band of plucky adventurers did it right (as an example, the scene where Serge uses the Mastermune to time travel to the burning of Lucca's orphanage and save the kids there
should have sent someone to the Darkness Beyond Time, because that's how Cross told us it works, but it doesn't dwell on it). I think that this is a mechanical failure of Cross' story, but it's also a piece of how Cross was kind of always going to have that baked in resentment from Trigger fans because of how it chose to follow up a beloved story with new ideas that were not necessarily incompatible, but rather were never intended.
Chrono Cross isn't, like, Boruto or whatever, where the happy ending of the original series still happened but now there's this new thing going on with new characters. It's explicitly a story about how the past heroes failed and in a way made things worse in the long run. There's no getting around the fact that the heroes you loved from Trigger are, per Cross, responsible for dooming entire timelines because you wanted the mayor of Porre to give you the Sun Stone. If, say, Crono showed up and died heroically to help the party (and he did because actually Crono is Miguel ask me why) that would definitely still piss people off but it would be seen as a much more fitting end for this character we love, and whether or not this is a good or bad story choice for Cross to make we really tend not to see it.
I'm also not sure how to tie the fall of Guardia into this exactly, beyond that Chrono Trigger DS reveals that Dalton, who was flung through time because of the gang, was the one who spearheaded it, but there's also a point to be made about how Cross turned the fall of Crono and Marle's home into a minor footnote. This tends not to happen in sequels and at the end of a story we kind of end it assuming that everything just kind of worked out for everyone and nothing bad will happen again, because if it did then we'd get another story out of it. I think this is why we tend not to get much in the way of sequels to massive RPGs about world shaking quests, because if another one happens six months later it kind of makes you wonder why you're bothering.
The fact is that Chrono Cross told a story that was built at the expense of Chrono Trigger and that's not a dig at Cross, that's just what it wanted to do and condemned the original heroes to make that point. It does lowkey nettle me when blokes go "ugh you're just mad that Crono died get over it nerdlinger" because even apart from that being a big enough deal to annoy someone, Cross is explicitly, textually, about the failure of Crono and his friends. If that's your thing go ahead, enjoy what Chrono Cross has to offer, but it's not surprising that someone doesn't want to engage with new material that starts with a Bad End for the last game.
It's also why you've got literally zero fans of Chrono Trigger DS adding those tie-ins to Cross, because Chrono Trigger told one story, Cross told another, and Chrono Trigger DS made them awkwardly intermingle when Trigger just wanted to go watch its Dragon Ball fansubs while Cross wanted to sit in a dark room listening to experimental music.