Why nuclear shells would not end naval competition

Would nuclear-armed shells fix a fleet by making every rival unwilling to challenge it?

No; opponents could seek countermeasures, doubt the weapons would be used, or acquire nuclear arms themselves.

Equipping a fleet with nuclear shells would not make every challenger disappear. Rivals might believe they could prevent the weapons' use, survive the threat, or obtain nuclear arms of their own. The supposed superweapon would create a deterrence and proliferation contest rather than a permanent monopoly. Possessing an extreme capability does not guarantee an uncontested strategic position.