The problem is that with the Burkes, we’ve continued to cram more and more and more stuff into their hulls. While there has obviously been size creep in classes (the Zumwalts are physically longer, wider and taller than some battleships that fought in WW2), that still doesn’t mean that there’s room to stick a reactor and power generation system into an existing destroyer class.
I don’t disagree that you can make a 10,000 ton nuclear surface combatant. I am just saying that it would have to either be a completely new design or a massive redesign of the Burke - the latter of which would be rather pointless as the Burke design is getting very long in the tooth and is absolutely inferior to newer designs like the British Type 45s (post engine/cooling fixes).
Agree ... I think “completely new design” is the only way to go. The Enterprise, and then the Nimitz class CVNs were designed from the keel up to be nukes. Same with SSN and SSBN subs, and with the 2 or 3 classes of CGNs. And to be fair, the Virginia class cruisers (CGN) were built in a totally different (and much less electronic) time. If we’re going to do CGNs again, trying to force-feed a reactor into a Burke or Ticonderoga hull would be madness.