Can you imagine ever house with 10 wire pairs coming in from the street, one from each utility?
Competition on distribution or transmission is simply not going to happen. But it can - and should - happen on generation, as it already does in a lot of markets around the world.
Once you have a distribution network or a transmission line in place, nobody will build a second one. It doesn't make any economic sense.
Even if it was a complete laissez-faire (a bad idea, IMHO), there would be no competition on transmission lines and distribution networks.
But I do agree with more competition, particularly on generation. And you can make it better by decoupling transmission from distribution, and forcing the separate operation of each, plus a state-managed electricity pool, resulting in customers buying either from the pool or directly from generators.