Carry potential in any game mode but SR is awful

And that's why you'll always return to summoners rift.

Twisted Treeline, ARAM, and Nexus Blitz all happen on very small maps that promote team fights and skirmishes. There's a severe lack of objectives(or reasonable objectives in the cause of NB) to take as well as a lack of map space for you to rotate through. It's mostly team play, there isn't really any means to macro or hard carry.

For ARAM and NB this really isn't the point of either, they're fun game modes. For TT, that's debatable. The issue is that there really isn't anything for solo players to play even semi competitively besides SR.