What people need to understand about the cycle efficiency is that when you mine uranium, the fissionable part of uranium (U-235) is only 1% of that uranium, the rest is nonfissionable U-238.
Thorium is about twice as abundant as Uranium (all isotopes). The MSR uses Thorium to create U-233, a fissionable but not naturally occurring Uranium isotope.
So the "unlimited energy aspect" is that about 200-300x more breedable Thorium exists than fissionable U-235.
A MSR nation could also try to breed U-238 into plutonium, which would provide another 100x more breeding stock, although LFTR never talked about U-238 breeding. IIRC the plutonium may be difficult to handle because of gamma rays, but I don't recall exactly.
While I don't have confidence that even LFTR/MSR reactors can get economical enough to challenge gas peakers, it may be possible to make truly price-competitive MSR electricity with the right modular design. I wish the Chinese the best of luck, because if they do it will spur the rest of the world to adopt this about-as-clean-and-safe-as-it-gets nuclear design.