When I first started watching, and even as a beginner playing, it made no sense. However, once someone explained it to me (like you described)... it made perfect logical sense. Regarding the scoring, I was accustomed to other sports where certain actions had values associated to them. Basketball: Free throw=1, inside the arc=2, outside the arc=3; Football where safety=2, FG=3, TD=6, and point after 1. There wasn't that "Action = Set number of values/points" that I was accustomed to, and until someone explained that to me... it didn't make sense at all.
Edit: (Not to be hinting that you, specifically, need things explained, or you don't know the game/scene, or anything derogatory... just saying that new stuff to new people = rarely makes sense until explained is all)
But, to me, the starter/counterpick system makes logical sense.
1st game is played on a stage that presumably gives neither player an advantage, or is one that both players can agree on (meaning that both players accept and are ok with any inherent advantages a stage may provide). Striking is done to get to presumably the most neutral of stages, as its reasonable to assume that both players will strike neutrals that lean to his opponent's advantage.
2nd game is played on a counterpick stage that presumably gives the loser a boost, like a handicap in bowling. I see it as a level of sportsmanship, and/or to possibly cover the fact that the neutral wasn't really neutral (which, if this is something that is a repeatable phenomena to where one char has a distinct advantage on a neutral, the neutral should be stricken). However, this boost is partially offset by the winner banning one of these CP stages. The loser gets to change their character to increase the handicap, while the winner gets a final choice in character to once again level the handicap.
3rd and subsequent games are played as the 2nd. The 1st game's winner will have the "counterpick advantage", wherein their victory in the 1st game is 'rewarded' with the ability to put themselves in a favorable position should they lose in a less-favorable one (their opponent's cp.)
Its a mini-game of rock/paper/scissors, give-and-take, and sportsmanly offsets. To
me, it makes sense, and ultimately balances out. It may not for you, and for many others. That's not an insult or knock or anything... merely just a different opinion. Because of that, I'm all for learning about and possibly introducing new systems that make sense competitively.
Also, liked your post due to the approach that the current system may be defining the meta as opposed to it growing on its own, which I see now was the intent of your OP and is an insight in its own right.