Any kind of paid exclusivity talk is fan fiction. We don't have any evidence that either of Persona 5 or SMT5 are paid timed exclusives. Maybe they're not? Atlus really did want to separate the fanbase?
There are enough timed exclusives out there where we know of said exclusivity being tied to some kind of deal, be it monetary or otherwise (marketing, distribution, you name it; ultimately it's about money all the time). See Forspoken, FF VIIR, XVI, or recent Bethesda games like Ghostwire or Deathloop. When it comes to Atlus games, sure, yeah, the exclusivity talk is purely hypothetical due to the lack of any kind of detail regarding potential deals -- if there were any to begin with, that is. Then again, we had Nintendo publish SMTV (in Europe at least), so we have at least
some indication that they were involved with the game, whatever the extent might have been.
What you were describing with Nintendo and PS battling it out over Persona exclusivity in the future and how both of them might end up getting their own platform specific releases --- there's no indication of any of that, thus: pure fiction in my eyes.
The others in this thread have delivered good arguments already as to why it's more likely to see Nintendo stick to (timed?) SMT exclusivity. I just don't see any basis for the hypothetical scenario you've outlined before other than "Persona is more popular, so that should be what Nintendo should be fighting for". If they followed through on that logic, they wouldn't bother with many other smaller projects from third parties, either.
That's not to say that they're not trying to have Persona be a regular franchise to release on Nintendo hardware, but that doesn't mean they'll start an exclusivity war with PS over it or something like that.