The repeats of old shows are never as many as people make out - it's a bit like that old "the weather forecasters always get it wrong" myth. The "running repeats" (stuff shown again on BBC3 &4) is industry standard now.
I'd love them to ditch eastenders but I wouldn't hold your breath. Overall I think the balance is okay across the channels and it's wonderful to have somewhere you're guaranteed no interruptions from adverts.
The licence fee isn't the sole income though. The commercial arm, BBC Worldwide, generates income from dvd/merchandise sales. I don't know the figures though, or if any/how much is ploughed back into broadcasting.