Skyrim was a rebelling province of a long established Empire not a bunch of wildly different survivors of a nuclear war.
The Fallout New Vegas faction reputation makes more sense especially if there are more than two major factions.
I do think Karma still has a use as a general reputation that would have a minor impact on factions that knew you and a greater impact on factions that didn't know you provided they were not isolationist.
Even if you are the golden boy of a faction there are some things that will cross the line with them.
That some thing may be very different between various factions and certainly they would take any rumors from your enemies with a grain of salt.
But if you have enough smoke from enough sources you get the Cosby effect.