The roads that aren't toll roads would be paid for out of the profits from toll roads. The company would have to hire employees to build or maintain these extra roads wouldn't they? Eventually, and hopefully, the market will winnow out the small guys creating an oligarchy or even monopoly with certain communities (although doubtful over a whole state). Contrary to the robber baron and anti-trust myths of the late 19th century, it would be a win-win situation for the companies and the users (see Northern Pacific Rail as an example)
sigh... But when I want to access someone elses toll road from one of your access roads for a different destination I'll be routed out of my way, then have to pay for the inconvenience by way of YOURs and who knows how many other toll roads.