The flaw with this reasoning is that a 9-ball match is not one game but a set or sets of individual separate games. Each game of 9-ball in a match is a separate game, unlike say, straight pool. That is why someone should not automatically be able to continue their turn if they won the last game and then do not make a ball on the break. The previous game is over so there is not reason to have any right to a "free" break in the next (and separate) game. If you want to play where the guy at the table at the end of the previous rack gets to keep playing, just play straight pool.
What happens if the player does not make a ball but doesn't have a shot? Should he get free relief since the break not being a skilled shot, it is not his error that he is hooked after the break. Perhaps the player should be allowed a clear spot shot?
Also, by your way of reasoning, there should probably not be any alternate break rule allowed, only winner breaks.
Part of the reason for alternate break is to afford a more even match or at least a match where each player gets at least some number of chances. Perhaps this is to make a TV tournament more interesting. From a viewer perspective it probably does make for a more interesting, or suspenseful TV event. I think it is a little more equitable for each player to get some chances to perform in order for a winner to be determined, and I think alternate break lends itself to this than winner breaks.
Lastly, if you want to eliminate more luck from the game, there should also be a call shot rule for every shot.