The problem isn't games being short, is the snowball

Short games are actually better because not everyone has the time to play a game that lasts so much time, especially if that person is playing in something like an internet cafe or a lan house.

The real problem is the snowballing, Riot is making games shorter by making them more snowbally and one-sided, which is unhealthy. Short games are actually more fun than long games, but not when you are stomped (or the enemy team is stomped) and have no chance of comeback. When you can't even get close to farm without being chunked for one third of your HP. When it isn't even 10 minutes of game and the enemy already has destroyed two of your towers and have a dragon.

Please note that a game being fast paced is completely different from a game being snowbally. Look at other game modes like ARURF or Ascension. They are fast paced (compared to common games on Summoner's Rift) but aren't snowbally. You will not instantly lose once the enemy has even a small advantage.

Unfortunately I don't know how to make the game more fast paced without increasing snowball potential, but I am pretty sure that there is a way to do that. I am yet another player that got tired of one-sided games.