The "Starfleet mostly sits in mothballs in peacetime" concept is IMHO dubious, because most of Starfleet's duties are peacetime ones
We saw little evidence that older, TOS movie era ship types would serve in secondary roles in the TNG era.
Yet if there was a surge of ships for the Dominion war, activation of idled units is a more likely explanation than construction of all-new ones, as we virtually never saw ships with "wartime" registries, that is, registries higher than those of the prewar DS9 and VOY hero ships. And we never saw ships under construction in that era - only older ships under repair in the prewar flashback scene of VOY "Relativity". Arguably, starship construction is such demanding and time-consuming work that a mere half-decade war won't see significant numbers of new ships completed; peacetime pressures are already so high that there cannot be appreciable increase in production speed and volume in war
I agree - I think Starfleet is at full strength in peacetime - it's not that I think it's mostly in mothballs, I just think it would make sense to store the previous generation of ships when they are replaced. Powered down they wouldn't deteriorate and as you can see from the number of Excelsior class ships in TNG it must be possible to retrofit new sensors, propulsion, weaponry etc.
Older ships may not make the best frontline warships, but in wartime for planetary defense, convoy escort, troop transport, resupply and a multitude of other roles they would be invaluable, and free up the modern ships for other duties.