Honestly, it's mostly the invisible plane that I can't get past. Get rid of that, and I'd be way more okay with the character.
Well, that's easy. It's hardly an indispensable feature. The modern version of Wonder Woman can fly under her own power anyway, so she has no need of such a thing. In the animated Justice League
, WW didn't use one, although she did acquire a cloaked aircraft by the time of JL Unlimited
Would you be okay with it if it were done the JLU way, as an aircraft with a cloaking device, rather than a transparent aircraft where you can clearly see Wonder Woman sitting inside it?
To me the plane just seems like a very odd "power" for her to have. It doesn't fit with the rest of what I know about her. She is a character based in myth and magic. Giving her an airplane would be like giving Thor a motorcycle or having Batman ride around on a magic carpet.