The reason there is a mandatory 20 minute timer is because most games would end at 10 minutes if you could surrender then.
The vast majority of games are decided in 10 minutes and playing it out is a waste of time.
But the game is intentionally designed to invest you in that 20 minutes, and most of the time you end up stuck in losing games because the enemy team wants to feel powerful and won't push objectives, but will starve your team in their base, while cleaning house on xp/farm.
Rinse repeat till they are 18, full build and have nashors then they come crush you.
And realistically, this was all decided at the 10 minute mark, because Riot doesn't want to re-balance and gimp all the snowball champs, because that's all anyone plays.
So the bottom line is, at 7 minutes, you've got two lanes losing, there's no reason to continue.
You would literally spend more time in matchmaking than in game after a point.
When it gets down to it, the game play has become stale and uncompelling, because there is never anything NEW added, and all the same problems are still there.
Seriously, why would you ever invest more than 10 minutes in a losing match?
The REAL issue is that you are even IN a game that you no longer want to play.
I know this frustrates the hell out of me, and its pretty much why I lose my cool.
You sit in Champ Select bickering about who is doing what, get into a game with the same handful of overplayed champions, you either win or lose your lane, and your team mates either win or lose their lanes, and then whoever did better overall in laning goes on to win the game.
The entire game after laning is a complete waste of time because 9 times out of 10, the game is already won.
The only reason it exists at all in its current form is so that people can feel relevant and powerful, meanwhile 5 players get beat on for 10 minutes waiting to surrender.
The laning phase IS the game, the rest is more like an afterparty.
When dealing with equally driven players of comparable skill level who are actually invested in winning the match instead of just racking up kills, sometimes it is possible to turn it around, but usually not and it still takes the correct team comp along with poor play by the enemy team.
Bottom line, the game really isn't very fun, it's actually incredibly stressful, and that isn't really good design.