Crying "monopoly" with the NBN is a tad misleading. Only the physical infrastructure (the fibre optic cables in the ground and associated switching infrastructure) is part of the NBN monopoly. Any ISP or telecoms company is free to provide services on top of that.
Anyway you're not going to get competition on basic physical infrastructure like this any more than you will on the water and sewer pipes, roads or electricity wires that lead to your home. These are all natural monopolies, they haven't just been legislated into existence.
The private sector never built anything like the NBN for the simple reason that the return isn't enough. It'll still pay back the investment the govt. made, it just won't make the kind of profit that'd be needed to entice private investors to stump up $37bn.