Something that every single league player wants...
I don't want that because it is pretty much useless.
Your ability to 1v1 and lane is an exceptionally small part of the game and completely discounts the importance of teamfighting, rotations, objective control, and wave management (among other factors). In addition, a large portion of the champion pool would be outright unviable in such a mode since their strength does not lie in laning, but in other factors of the game.
1v1 queue. Nothing is more aggravating in gaming than knowing you can play but, being held back by a team.
Teams do not hold players back in the long-term. If you deserve to climb, then you will gradually climb to your appropriate rank.
I think I speak for a huge portion of this community when I say: PLEASE DO THIS! With 1v1 ranked ladder of course.
Considering they just removed Dominion to reduce the number of maps they have to support (or at least, that's what they say), I really can't see them adding a 1v1 map back into the game. At least Dominion had its own meta and playstyle to support a large number of champions and builds; a 1v1 wouldn't.
At most, I could see them bring back Snowdown Showdown for a few weeks.