Why F3 is a better carrier basis than Nelson

Could the Royal Navy base every carrier and battleship on a modified Nelson or Rodney hull?

Not effectively, because the Nelson design is too slow; the 29-knot F3 battlecruiser would be the more plausible common-hull basis.

A common carrier and capital-ship hull still has to meet the carrier's speed requirement. Nelson and Rodney are too slow to provide that basis without a major redesign. The unbuilt F3 battlecruiser offers a better alternative because it was intended to make about 29 knots. That speed does not prove a complete common-hull program would work, but it makes F3 a more credible starting point for the audience's British version of the scenario.