Reactor-accident politics in carrier operations

Would political concern over a reactor accident keep nuclear surface escorts too far from combat to be useful?

A nuclear carrier group already takes a carrier and usually a nuclear submarine into the same operational risk.

Political fear of a battle-damaged reactor could keep a nuclear surface escort away from danger and reduce its combat value. The same concern already applies to the nuclear aircraft carrier it would escort. A carrier group will also usually include a nuclear-powered submarine. The British example given here includes at least two destroyers and two frigates, often with allied ships raising the surface force to seven or eight vessels, plus supply ships. A nuclear cruiser would add another reactor to an already nuclear formation. Its capability and cost still need to justify that addition.