While I can agree that it's a good idea in principle, there's quite a few issues that would likely pop up in practice.
If you're allowed to report before the game starts, but the game proceeds as normal anyway, the situation hasn't really changed. Yeah, they've been reported, but you could have done that after the game. The only real benefit you get out of it is if you queue dodge, because then at least an obvious troll got reported, but you'd still be stuck with the leaverbuster suspension. On the flip side, this system would no doubt be abused to no end to report legitimate players using off-meta picks while still in the champion select stage, instead of the current system which forces players to wait until the end of the game and see whether the player was really just trolling or if they were legitimately playing and just using a strange pick.
The option of reporting before the game starts cancelling the queue is even more prone to abuse than the previous one, although it would no doubt have some pretty strict punishments in place for those who abuse it to queue dodge without penalty because their champ got banned/picked by the enemy team, they didn't get the exact position they wanted, etc. Even with that, though, punishment would not be instant and would have to be severe (much more severe than the current Leaverbuster system) to actually dissuade abuse of the system. Having such harsh consequences as backlash for a false report would have severe consequences to the false positives that turned up (situations where a player legitimately believed another to be a troll/toxic player from their attitude, but the system/rioter charged with reviewing it disagreed) that would be undesireable.
TL;DR: Such a system would be nice, but would be so prone to abuse that whatever positives might come out of it are vastly overshadowed, which in turn would make it a low priority feature to add at best.