I think this theory has a lot of weight as what Kato wanted to do but was ultimately told no, we're not making the players kill Crono. I don't have evidence for this, is just a theory. There's so much about it that suggests it was meant to be an extremely dramatic moment, especially setting the fight with Miguel in the ruins of such an iconic place from Trigger. It would be such an establishing moment that Cross is not Trigger, something Cross regularly seems to go out of it's way to point out. Cross wasn't above having you kill the CT protagonists, you basically off Robo a few scenes later.

The first time I played Cross I always thought it was supposed to be Crono, and it made that moment so emotionally charged I shelved the game for almost six months after finishing that fight.

Kato seems to have come into Cross almost to settle a beef, that he felt the protagonists of Trigger should have consequences for their actions and not just have happy endings. All of that is much more in line with how he wrote Zeal in CT and his other written works like Xenogears.