The problem with this argument is that there are other fighting games out there, good ones at that, that also have alot of this. The Street Fighter IV series and the Guilty Gear series come to mind. Now while there has been some pushback against it in the former (hence DWU in Ultra), the latter is basically all about set play/oki, to the point where it's a series trademark.
I am not familiar with Guilty Gear, but I do know that Capcom has implemented the delayed wake up system in Ultra Street Fighter IV, as you stated. The game now revolves around high damage conversion in footsies, best exemplified by Daigo's Evil Ryu. Even in the prior Street Fighter installment, an Akuma player, for example, had to know how to safe jump an opponent and perform various option selects. A Batgirl player does not have to worry about these intricacies. Also, Akuma's mix ups were and still are limited to right side versus left side mix ups (i.e., cross up versus non-cross up). Batgirl creates an addition mind game that is up versus down (i.e., overhead versus low attack). The comparison is a false equivalency. Batgirl presents the simplest type of mix up in a fighting game. The only thing simpler would be an infinite combo. A Batgirl player would never have any success using Akuma. The character is too complex for them.
Batgirl would be tolerable to some extent if characters like Aquaman, Batman, Black Adam, Deathstroke, Killer Frost, Sinestro, Superman, and Zod had never been normalized. Fight the bullshit with the bullshit. But this is the NRS community that we are talking about. Everything powerful about zoning must be patched first to appease the scrubs. That is why the games will never be balanced.