I love 2vs2 as you have to play with your partner and you gonna lose if you just play for yourself. The greatest problem are surge mechanics and similar abilities if used with 2xSame faction. Lichs are one of the strongest themes in play(only my opinion) and they are totally devastating in 2vs2 A Solution would to make Surge mechanics only count owned champs and similar abilites affect only owned champs That would on one hand balance 2vs2 without effect on 1vs1 but would on the other hand drain the fun out of 2player themes.
People do not care about 2v2 because there is so much wrong and/or broken with it that cannot be addressed outside of nerfing runes for 1v1.
I know that, but if we leave aside the hate for a while it'll be easier to try to fix that problems. Grillado makes exellent points on the owned specification that'd make a lot for it.