I'm going to quote a few things from Brawl Minus's main website.
"Brawl- has as one of the first and foremost goals, "fairness". That is, no character should be overpowered, and no character should be underpowered. We don't want another Street Fighter 2 where there is one character who kicks the crap out of everyone else."
"We will try to balance everything by taking everyone and putting them all on the level of, approximately, Akuma from street fighter 2 turbo. Expect crazy action and moves you may never have seen before."
Going by these quotes, making Pichu deliberately inferior to Pikachu goes against the intended goals of the project. He should be as good as anyone else, joke character or not.
Pichu was never intended to be inferior to Pikachu, but different from Pikachu while on equal footing. His self-damage was supposed to be a trade-off for his strength, but he's not strong enough yet. As always, we have plans to change up Pichu for the better even more, and will be looking into his mechanic as well.
I dare you to speed up Link's jabs by another 2 frames and buff percent done by 2% each, make utilt a bit faster/stronger, make his dair stronger, and buff grounded Spin Attack by like 5 KBG, but Spin Attack does 10% self-damage per use (except in air), utilt does 6% self-damage per use, dair does 5% self-damage per use, and each of Link's jabs does 3% self-damage per use [the numbers are high because Link is heavy). Oh and make Sonic's boost do 1% to him every 6 frames it's in use.
That way you can have a little risk in your games.
If that's not what you're saying then none of what I said applies.
It's not a risk because there's nothing you can do about it.
Again, pichu is actually really good. However it shouldn't self damage because as stated in the OP, that punishes the player for doing well. (Unless only her strongest moves did it) The aura system is meh, im down to get rid of iy
As an idea that both keeps the self damage and rewards pichu for doing well, have the self-damage from pichu's electrical moves be put into a buffer. When pichu connects with an electrical move have it heal pichu for some of the damage in the buffer (in terms of flavor pichu builds up static by using moves and dealing electrical damage removes some). To expand on that you could add bonus damage for removing more static, give a way to turn normal damage into static, or even grant new abilities only available (or only after removing) over some amount of static.