Obviously, for characters that are already spirits they can just use alternate artwork (or even just the Smash artwork if there really is no other option). I'm... not too keen on outright removing the original, though. Sure, it might seem odd to see Ashley fighting her own Spirit, but at the end of the day, I want DLC to feel like an add-on rather than a replacement for something already in the base game. As for Assist Trophies, I feel that can be a pretty simple workaround: just don't spawn the assist character if that character is in play (with the exception of Spirit Battles that force a specific assist onto the stage).
I'm probably not the first one to present those ideas, though. However, I think I have something truly new to offer... Now, bear in mind, this idea is a little... out there. But, fitting with the previous idea of "don't spawn the assist character if that character is in play", what if in the second season they introduce an update that brings back previous Assist Trophies that were already promoted? I'm talking Isabelle, Dark Samus, Little Mac, etc. But here's the best part... in that same update, they create new Assist Trophies for other veterans as well! Maybe, like, a Mario that acts more like his traditional games by stomping on your opponents. Obviously, this update would have to be introduced after an assist has been promoted to full-on playable character.
Like I said, my idea is pretty wild, but maybe someone here will appreciate this...