While I understand that the US is a much larger country, and to some extend have different requirements and the same things may not be profitable, why not "simply" require open access.

The Danish fiber infrastructure is in large parts build by the power companies, because they where doing the digging anyway. Other parts are build by ISPs, or as municipal projects. Once the fiber, or cable, is established all ISP can use it. This ensures that all companies have almost the same coverage and can offer their services around the country, but cutting down on the cost, by preventing parallel infrastructure from being build.

The areas where it's not financially viable to build out the infrastructure, like some islands, the municipalities or even the government, can step in an build the infrastructure, or pay a company to do it, and then leave the services to be offered by the ISPs.