Remake Mechanism is useless in most cases
So I just got a game where my adc (Ashe's) mouse died. We couldn't remake as she did in fact connect. However this caused us to lose because we were down a player. I would suggest an added remake mechanic where you can remake if say 6 people voted yes. (Prevents remake from bad team comp) This would improve the League environment as it encourages sympathetic action for situations like the one above. If there is an obvious troll in a game a remake can be called and everyone can report the troll. Also it would encourage the honor initiative.
Obviously the 6 vote count can be made into a different system such as 3 from allied team and 2 from enemy team (prevent duo queue trolling).
HoN has a similar mechanic if I recall and overall it works out nicely.