Why the Iowas could not serve indefinitely

How much longer would the Iowa class remain in service if the Cold War continued?

Probably not very long beyond the historical period unless the US had deliberately preserved them and their support industry decades earlier.

Repeated activation after 1945 consumed hull and machinery life, while the 16-inch guns eventually needed relining or replacement by an industrial base that no longer retained the capability. Keeping the ships into the 2010s would require an implausibly farsighted decision to preserve them in the 1950s while running older North Carolina and South Dakota classes instead. Maintaining older battleships could prolong the supporting yards and spares network, but practical wear still sets a hard limit.