This would never happen. If roads were privatized they wouldn't care about connecting as many homes/business as possible, they'd only care about building roads where it was the most profitable for them and even then any roads that made less money would be left in increasingly poor condition.

It wouldn't leave taxpayers off the hook either. Governments would have to spend taxpayer money to incentivize private companies to build out in "unprofitable" areas, but those roads would be kept in the worst conditions of all (assuming that companies didn't just repeatedly promise to build them, only to pocket the taxpayer's money while providing nothing)

Some services are worth enough to the public good that profit shouldn't be the only consideration, and some are worth so much that profit shouldn't be the goal at all and instead those services should simply strive to do the job required for every citizen with as little genuine waste as possible.