Our navy has the same vulnerabilities. Every escort vessel in a CVBG is conventionally powered. No escort vessels - no go.
Except they have one fuel powered carrier and less than a dozen nuclear submarines. Good luck getting within strike range undetected before being obliterated.
Exactly this - the Nuclear Navy has been decimated since the 60s and our destroyers and cruisers require oilers to refuel regularly. The only remaining nuclear powered units we have are carriers and submarines.