I'm gonna ramble a bit here, because Glowsquid brought up some very valid points about this 'importance' deal and it made me think, maybe the problem people have has more to do with what will happen to the series if Ashley takes over and that's why they use that as an argument?
It's a dumb concern because a few 3DS themes and badges can't compare to the money a game would make, but let's imagine she does end up becoming the mascot of a merchandise series and it turns out to be more rentable for Nintendo than keeping up Wario Ware games.
Wario was reduced to a wa version and his own series -where his character actually had some spine- was forgotten, and Mario became a clean-cut summary of what it used to be. We dislike what the series are now because what they used to be before was pretty damn good, and the potential a new game with that old spirit would have is huge. So it's not about 'preserving the integrity' of the WW series or what bunch of pixels deserves more love than the other, it's more being afraid that this slow change of focus would lead to good games not being made; not because the franchise didn't offer potential, but because pandering makes easier money. The basic idea that it gets ruined for factors other than its own quality, to put it simply. It happened before and it could easily happen again, so the concern might as well be valid, even if a bit too extreme given the little info we got as of now.
But now, let's imagine Ashley eventually gets her own game, and it turns out to be fucking GREAT. Would you be pissed off Wario Ware didn't get the recognition? I sure as hell wouldn't, because my priority here is that we get more good games. I'd prefer a good Ashley title over another Game&Wario.
Again this is all hypothetical rambling since I'm trying to make sense of it from a gaming perspective more than fandomy personal tastes, but yeah. I feel people are defending the characters as a big aspect of a good game rather than them being important on their own, if that makes sense? taking them away in favour of a single one might be just another way of 'flanderizing' a series that would have been perfectly fine otherwise. But eh, like I said, it's all down to how it's handled.
Whatever happens (if anything happens at all) I just want good games out of this :c