A prime example of peacetime ops is anti drug running patrols such as those carried out by the USN, USCG, and the RN and RFA in the caribbean. Some have criticised the use of a large, complex and expensive warship such as a type 22 frigate or an Arleigh Burke class DDG on relatively low tech missions like this, but Navies have to be very flexible and ready to meet any threat, large or small.
The US has a pretty large coast guard fleet, with approx. 1,400 boats and over 200 aircraft. The boats range from small fiber glass harbor patrol boats to the 3,250 tonne "high endurance" cutters, armed with 76mm cannon, 20mm CIWS gun, and helicopter deck.
Let's look at the largest US Coast Guard "gunships":
12 x Secretary class high endurance cutter
3,250 tonnes, 76mm cannon, 20mm CIWS, helicopter deck
13 x Famous class medium endurance cutter
1,800 tonnes, 76 mm cannon, 2 x 12.7mm machinegun, helicopter deck
14 x Reliance class medium endurance cutter
1,127 tonnes, 25mm autocannon, 2 x 12.7mm machinegun, helicopter deck
Since these ships are for the coast guard, they're all gun boats without missiles. But if they were actually built (or refit) as military ships, they'd be a fleet of 12 frigates and 27 light frigates. That's a larger surface fleet than most navies today.
There's really no reason for the USN to send out destroyers for anti-drug operations. The US Coast Guard has plenty of ships and aircraft.