Yeah, when comparing the base roster characters to all of the DLC fighters which were new to their respective Smash Bros. entries, there's clearly a pattern with how everything's structured.
To the point that, ironically, some of the most popular 1st Party requests have less of an opportunity than not-so-popular 3rd Party requests to join the battle in a Nintendo fighting game at this point.
Base roster picks have proven to be quite flexible, presenting a clear emphasis on including popular and/or iconic Nintendo characters no matter their current status within their respective Nintendo properties. Therefore, there typically isn't as much of a focus on 3rd Party characters in general at the time.
DLC picks on the other hand have proven to be more selective, presenting a defined emphasis on including characters only if they bring something new to the table. 3rd Party characters can pull this off easily, which is probably why they're favored during this time. Granted, Sm4sh's DLC was as unorthodox as it could get, since it began by dishing out characters who were already in Smash before. However, the last few picks (Ryu, Cloud, Corrin, and Bayonetta) satisfied this hidden quota for DLC characters moving forward.
Therefore, I believe that we certainly won't see them pulling Bandana Dee, Waluigi, or Dixie Kong out of a hat for no particular reason at all.
Heck, I don't even think popularity has anything to do with it, at least more than satisfying this particular quota of bringing something new to Smash.
Fire Emblem is pretty lucky since it has a rotating cast with new protagonists for each entry, because this provides a perfect opportunity to pick someone fresh and new from that series for the roster during the DLC period. Min Min had the benefit of being a Nintendo IP which hadn't been properly represented in Smash before the DLC period began. Not to mention that ARMS came out before Ultimate, unlike Splatoon and Sm4sh, so everything worked in the Smash Team's favor. But most importantly, the quota was fulfilled.
The same can't easily be said for those other three characters I mentioned (or certain other 1st Party requests), unless there is something from their own respective franchises of which they themselves could promote. Which might sound easy at first until you look back at how Fire Emblem, a franchise already represented in Smash, brought even more representation into Smash through DLC: It was fresh, it was specific, and the character had a starring role within that specific game.
Let's compare this logic to my most wanted 1st party character (and most wanted in general), Bandana Waddle Dee.
The latest core entry in the Kirby franchise thus far was Kirby Star Allies. Could he use that as a ticket into Smash? Let's see...
Is the game in question fresh? Compared to even Three Houses, not exactly.
Is the game in question specific? Yep, it wouldn't be promotion in the form of a range of games.
Does the character have a starring role? It's debatable, since Kirby was clearly shown as the main protagonist from the start of the game's first cutscene.
Additionally, there is at least one music track from the game which is currently in Ultimate, so there's already representation for the game beyond Spirits.
Therefore, this wouldn't be a good base for Bandana Dee to stand on and thus he wouldn't fulfill the quota.
The solution for characters like Bandana Dee would be to hope that a fresh, new game for their respective franchise comes along during the DLC period, of which they also star in as a main playable character. (Oh yeah, the emphasis on DLC protagonists also convinces me that there won't be any villains in any Fighter Pass, unless they're somehow main playable characters who stack up to the main protagonist, but that's another topic).
Anyway, if anyone wants to dissect any particular point(s) and have a little chat, feel free. Otherwise, I just wanted to place my thoughts on the debate between 1st and 3rd Party character.