Ping!
The problem is we're still talking vertical takeoff with 100% of the required fuel and oxidizer from ground level. I know you're promoting nuclear, but that's never going to happen politically.
By using air for oxidizer for roughly half the acceleration, you drastically reduce the required weight for oxidizer, and thus reduce the fuel required and the size of the vehicle that must carry it, thus saving even more fuel. The savings snowball.
Aerodynamic lift up to 100k feet is far more efficient than vertical takeoff, saving even more fuel, and allowing smaller engines.
Taking off with only partial fuel, and tanking via garden variety Air Force tanker allows takeoff with even smaller engines than lifting the whole thing from a runway. An SR-71 can't even get off the runway with full fuel, and I'm sure a runway to orbit vehicle would not either.
The months required, if not years, for building/refurbishing very large rockets will run the cost up just as it did the Shuttle, which originally was supposed to have turn around times measured in weeks.
Yes, we need high lift unmanned rockets to get large components into space, at least until we can fabricate them on the moon, mars, or asteroids (which will be a long time from now). But human transport and resupply should be via some kind of Turbo/Ram/Scram/Rocket aircraft. Yes the development cost would be extraordinarily high. But until we build such a thing that can be re-flown within a day of landing, or less, then space flight will be only dreams and fodder for government pork.
No thanks.