Just give it time - this is how every hero's launch is. It'll get much easier in a few days.
There is no possible way to make your idea work. For one, you can't just restrict anyone from using a new character - you can't. Especially if we consider that we're talking about a character that has to be purchased. Second, it would not solve anything - many others would have "their fourth match", so it would still be decided on the basis of who's the fastest one.
I understand your frustration - for me, Anakin is the only Light Side hero who's not level 40 yet. I don't particularly like HvV, and it is also the most bugged game mode - so if I can't be Anakin (or Dooku on Dark Side), I can be quite grumpy, lol. That's a "fruitless" match for me: no character levelling, and the game mode doesn't yield a huge sum of credits, either.