> I kind of like the idea of every government function has two independent providers that compete for funding

This is what the current government contractor system looks like.

> and citizens could choose which provider to use.

And how would we receive these choices? Balloting is a government function... Should we ask Diebold?

I think you'd need a lot more than 2. It's hard to get meaningful competition from only a smaller number because it ends up being much easier and profitble to collude (see telcos/cable companies/etc).

Just vote with your feet.