I'm starting to agree more on the limited amount of mulligans, 2 sounds fine, and then if a basic isn't in the last mulligan it could revert to the current rules.
I can easily manipulate situations that are currently possible in the game to make the judge give a decision when stalling happens, and to be done in such an elaborate and extensive manner could be considered cheating which would end the match. However, I don't advocate unlimited mulligans anymore, so this wouldn't be an issue to come up, but I didn't change my mind because of this issue.
Just because it's always been doesn't mean it shouldn't change, Pokemon's already changed rules before, it's not above them to do it again.
I don't mind having a luck factor in the game, it's the unfair and unintended luck factor that I don't want in the game. Also I can tell you I and can more than likely promise Darth Pika ran
all of those cards you listed, and still lost.
EDIT: Chess is 100% skill, there is no luck involved whatsoever, unless of course I guess if a player starts random putting pieces into places, but then you would probably just win against that. Also, we're not talking about playing chess, we're talking about playing Pokemon, so I don't really understand how playing Chess is an alternative.