The problem with locking people out for specific amounts of time is that not everyone internet connection is perfect. If my internet went out for the duration of a game I was in (which it has 3 times in 6 months, hence 3 leaves on my account) I would be locked out of playing for 24 hours, or however long you might propose. Should I be punished for that? No. I may have screwed my team over, but I certainly did not do it intentionally.
As for auto-banning when a certain number of reports are filed, that could be very easily abused. Imagine you, perhaps, said something to the enemy team that they didn't like. They all 5 agree to report you, and you subsequently get banned although you may not have deserved to be.
Riot is working through the reports currently. They are aggressively banning people, and have stated that thousands have been banned already. Yes, leavers, griefers, afkers, etc. are frustrating. Unfortunately, thats the nature of competitive online games.
The best thing you can do is report when necessary, don't break any of the rules yourself, and set a good example for other people.