The problem is that even the latest generation submarine reactors are just too big to stick on a Burke. The Zumwalts are big enough to mount one, but we only built three. And then wasted a bunch more money on the LCS.
Flight III Arleigh Burke destroyer (DDG)
Length 509.5 ft, Beam,66 ft, displacement 9700 tons
Virginia class cruiser (CGN)
Length 585ft, Beam 63ft, displacement 9472 tons
Virginia class submarine (SSN)
Length 377 ft, beam 34ft, displacement 7800 tons
1) And the Burkes are destroyers??? LOL!
2) The Virginia class CGN were built in the 1980s.
3) I get that there are a whole lot of design differences between the two surface ship classes, but they’re of comparable size. A nuclear powered 10,000ish ton surface warship is possible. Whether it’s desirable is a separate question.
4) Virginia class subs were much smaller than Virginia class cruisers.