I think Master Chief's chances will stay about the same as they've been, which are quite good, just now the "hasn't been on Nintendo" shtick is counting its days and people won't be able to deny him anymore. I kinda wish he will have made it in before Halo hits a Nintendo console, just to stick it to everyone, but it seems more likely that we'll see some of the older games ported over onto the Switch successor.
Which hey, that's cool too, but it's just gonna perpetuate the same misconceptions... although we're certainly running out of viable or exciting characters who haven't been on Nintendo at that point. Maybe just like, Kratos or Gordon Freeman?
Although in all honesty yeah, of course having Halo games on Switch (2?) gives Nintendo another incentive to consider him. I just think the scale of the character, his status as Microsoft / Xbox's mascot, the apparent fan demand already puts him squarely on the radar as the most obvious next step for Microsoft. This is just gonna make his case look that much sweeter to everyone speculating about it.