To be honest, the "Series specific" break the targets idea is the worst of both worlds. You don't get challenges specifically tailored to each character's capabilities, and you don't get the ability to use any character you want for each stage. The only advantage would be aesthetics, which is honestly by far the most irrelevant and unappealing feature of the mode if you ask me.
I still think that character specific challenges are possible, if they are part of the project time from the start and don't use unique graphics for each character. But I'd seriously rather get Brawl's generic levels than series-specific challenges. Mechanically speaking, a series-specific break the targets would still have to be inherently designed to be playable by any character (at least within each series, which often have wildly different characters) but they'd just needlessly limit the characters you could choose. At that point I'd rather just have the ability to use any character.
I fully approve of the online Target Test creator though. And I feel like if they wanted to do something like that, they could easily extend such a mode to cover more than just Target Tests. Like Board the Platforms, Race to the Finish, or even mixing all three. If they did it and went all out with the damn thing, we could even have custom event matches, but that's kind of a crazy dream scenario, haha.