Why do you feel this way? Given the hyper-competitive nature of some players, what i am concerned about is:
1. Player X (overly competitive) matches with Player Y (a normal, decent chap)
2. Cards are assigned randomly by the game.
3. X does not like this set. He refuses to take a turn, thereby (under your system) getting a "free" avoidance of cards that she does not like/is not skilled at playing.
I'll note that your proposal would give a HUGE advantage to the player who gets to go first. He would have the power to end the game with no penalty, while player #2 would be forced to play with 'bad' cards.
I'll also note that this first player could also force this end-of-game if he did not like his opening hand. Say, a 5 (or 2 draw) in a kingdom that had no 5-value cards.