There is no business case for basic research, but if you stop basic research long enough you will have no business. The United States and its allies seem to have completely forgotten this.
It makes sense for big monopolies like Bell, or the CCP. The investment can be justified if the ones investing are confident they will be able to capture the value and not some competitor.
Bell Labs also served to maintain positive perceptions of the monopoly. Unix was famously developed despite the knowledge that AT&T would not be able to offer it as an independent product.
I don't see how it follows. Anyway it's debatable if the current system with antitrust laws is true capitalism. One of those poorly-defined words that people argue over.
This isn't basic research. The US has had this tech for half a century. There's just no reason to do it. Uranium is plentiful and cheap and arguably safer.
The fuel cost of a NPP has almost no impact on the NPP's operational expenses and a LFTR (like all liquid fuel designs) is a far safer design. Nobody in the energy industry has talked about the fuel cost in nuclear in 50 years. It isn't even a consideration when comparing designs. Waste volume, safety, politics, and construction labor costs are the factors which are considered (also temp of the heat maybe).