I could be wrong but I feel like Crash’s chances are a bit overestimated. If we’re just going by historical impact, I feel like other Activision/Blizzard series were bigger like StarCraft, WarCraft, and Diablo. Microsoft also has Halo and DOOM for huge iconic series. There is a strong argument that Crash’s rival mascot status on the PS1 could be enough though. I think a second RARE character has a strong case for a similar reason due to their connection to Nintendo. Crash also has fan support, which helps. Crash certainly still has a chance, I just don’t see him as the default most likely Microsoft rep.
I think Crash getting in would be due to demand, not the heights reached by his series, nor his (tenuous) connection to Nintendo. Third-parties aren't really included on that latter basis. It's just that having a connection can lend them demand, and that demand can get them included.
That's how Sonic, and Mega Man and Banjo did it. Because there are plenty of third-parties with some connection to Nintendo. That in an of itself isn't really enough, it needs to be leveraged into popularity. Look at the remaining Rare characters. They have a Nintendo connection, but let's be real, the chance of any of them being fighters is pretty small, as none really have much demand.
It definitely helps that Crash has outstanding fan support; Hell, I think he even got first place in the last SourceGaming megapoll. That said, you're also correct in that much of Microsoft's other IPs that they bought out are very impactful in the general sphere of pop culture. I think it'd be something of a Banjo situation, where Crash would be chosen for his ties to Nintendo (albeit as a former rival and not a former 64 exclusive) and fan support than hard sales.
Truth be told, though, I don't know if Crash would be chosen over another Microsoft character; As in, I don't think characters from the same company are necessarily mutually exclusive. Nintendo managed to negotiate Simon and Richter together on top of getting Snake back, and assuming they weren't negotiated for in advance during Smash 4's DLC cycle, they probably had to negotiate to get Mega Man AND Ryu back at the same time, on top of getting the rights to Ken. I don't think it's likely that we'd Crash and, say, Doomguy in the same DLC wave, but I don't think it's necessarily impossible. If Nintendo sees two popular, influential characters from the same company who would both make a big impact, I think they'd go for 'em regardless.
Unless their owners say no, obviously. Maybe Microsoft would attach too big a price tag on both. But still, we got Banjo and Steve just fine on top of Cuphead, Fallout, Dragonborn, and Doomguy Miis, so I don't think MS is that hard to work with.
No, characters from the same company aren't mutually exclusive, and it seems entirely possible we get multiple Microsoft newcomers, they have a wealth to choose from.
But also, whether they are licensed at the same time or not is probably going to be on a case by case basis. Like, for base, I would agree that, like, Snake and Simon were probably licensed at the same time. But I think, based on how the content was distributed, Cloud and Sephiroth may have also been licensed at the same time, with one just being held. And then, even though they were in the same wave, I think Sephiroth and Sora were not licensed at the same time (I know Disney owns the license, but Square was obviously involved). You also have to wonder if a character like Bayonetta was licensed for both Smash 4 DLC and Ultimate simultaneously.
I think some characters are licensed further in advance of when they show than others, and also that they will be licensed in waves, potentially returning to the same companies later on. I think it's pretty highly variable, and maybe Crash would be licensed at the same time as Banjo and Steve... or maybe it'd be much later. It depends on the rollout and the unique deals between the companies. There's no one pattern, imo.
Also I agree MS probably will be amenable to cooperation, but of that list only Banjo and Steve were (probably) involving MS. Cuphead the IP isn't owned by them, and Vault Boy, Dovahkiin and Doom Slayer were, I would guess, licensed at the same time, prior to the Bethesda buyout.