Laying cables is really expensive. It takes a lot of capital and the return on investment is long-term. Two things that aren't very popular among Wall Street or VCs. Even assuming you undertook such a venture, Comcast/ATT/Verizon have really _really_ deep pockets. They can undercut any price you care to offer.
The idea that "regulation" is causing high prices is farcical on its face. There aren't enough schools and libraries to make any difference to the bottom line.
The market is uncompetitive because broadband is a natural monopoly. Just like roads, water, sewer, and electricity. The capital costs are so high there is usually no business justification for having more than 1-2 providers in a given area. There are a few exceptions but they prove the rule.
A "free market" in broadband would look much like the "free market" in electricity: Either the government or a regulated utility granted monopoly power by the government should run the fiber. Any ISP that wants to compete can hook up at the local CO. The equipment on both ends of that fiber can even be owned by the ISP so if new technology allows faster speeds nothing blocks the upgrade (the favorite excuse for pro-corporatist shills).
The big three have fought anything that smells like a free market tooth and nail, outright purchasing legislation at the state level to squash municipal attempts to do anything like this.
The funny thing is the big ISPs rely on government-granted taking of private property in the form of right-of-way to run their cables... something for which property owners receive no compensation. So much for "using our lines" as the ATT CEO likes to claim.