The /Remake vote is meant to mitigate the damage done by people who fail to connect or leave before a match begins - sadly, it offers no protection against people leaving as the match kicks off.
The Early Surrender is meant to allow players a (currently) unanimous vote to call the match lost - ten minutes in would be far too short to tell in most cases, so fifteen minutes is the margin where Riot allows people to determine - as a team - that the match is going downhill.
Then, of course, the 20-minute Surrender is there to allow players to call a match done via majority vote.
There is some good news, though - Riot plans to reduce the Early Surrender vote requirements from unanimous to vast majority vote (so from 5/5 down to 4/5, 4/4 to 3/4, etc.) sometime in the near future.