I wouldn't say unpredictable. We can form a reasonable idea of what they'll do based on precedent. Of course, we won't get it right every time, but we can definitely narrow things down.
With first party DLC, Nintendo leans HEAVILY towards promoting recent games. With 3rd party in general Nintendo almost exclusively has added characters from franchises with very high sale numbers and/or that are well established/classic. Literally the only exception to this has been Bayonetta, and she's practically a Nintendo character.
I agree. You'll see some people claiming the 3rd party characters all come from obscure series or aren't well known, but at least in the passes up to this point, this is definitely not the case. I think Banjo is the most out there / not as popular by today's standards, but the other ones are absolutely from extremely relevant or popular series.
If you look at any list of "Top RPGs for PS4" (or XBox, whatever), you'll find Dragon Quest XI S, Persona 5, and Final Fantasy VII Remake on it. I dare you to find another fighting game with as many releases and iterations as King of Fighters (okay, okay, Fatal Fury isn't
quite KoF, but it's basically the modern day equivalent and Terry is in all of them anyway). They might not be Smash Brothers or Tekken level successes, but there are dozens of them spanning basically all generations of games with a new one out soon. Steve needs no explanation, highest selling video game of all time.
Banjo, while being the character I've wanted since Melee, is the black sheep of the bunch. Sure, the games were good back on the 64 and among 3D platformers they're still solid, but there aren't any new games, the fan base is pretty age and genre specific, and it's looking like Rare doesn't have immediate plans to piggyback off of recent Smash success. (I hope I'm wrong, I'd love a new BK game!)
So yeah, the 3rd party characters are all big names, or at least all from big series. I think this meshes with Crash's chances just fine. Crash is to PS1 like Banjo is to N64, except Activision has recently in the last few years realized they can milk more $ out by rereleases, mobile games, and a new game. (I don't mean it to be negative, I just mean they realize they can monetize from Crash's name and character. And really, it should be that way, players just get attached to the character sometimes.)
It doesn't really bode well for any non established Indie (and even those that have been around a while like Shantae simply don't have the sales), any standalone game that isn't part of an umbrella franchise, or something that didn't sell well.
Now obviously Nintendo could be like "Hey, you know what, these characters from this series are really cool, we're going to add them", it's just that there isn't precedence for that yet.
And you're spot on with 1st party. While again obviously possible, so far every 1st party DLC has been from a game or series that came out in the last 5 years. I'm not going to count Piranha Plant (though you could, because they're in almost every iteration of Mario games, and there have been some new Mario games in the last 5 years, even if they're rereleases).
Now I don't know if Nintendo will continue to pull from the RPG genre in which case a Tales character would 100% fit in with picks, a platformer which Crash would, a Rhythm genre which Don-Chan would rep perfectly, etc. etc., but I would legit be colored surprised if we got a 3rd party character that hasn't had some recent success or is part of a franchise that sells well. Or a 1st party that isn't from a game that came out after 2010.
But of course, Nintendo can do whatever they want obviously.