Realised that most modern submarines (and some aircraft carriers) use nuclear power, but destroyers and frigates don’t. I don’t imagine it’s a size thing, so I’m not sure what else it could be.
In: Engineering
The biggest issue is that nuclear power is fairly expensive. While you no longer need to bring in fuel, it takes a lot of engineering to built a reactor and highly trained operators to keep it running safely. The [nuclear training program](https://en.wikipedia.org/wiki/Nuclear_Power_School#Nuclear_Power_Training_Unit) is one of the more grueling the US Navy offers, and each nuclear ship requires multiple officers per shift as well as a number of enlisted per shift.
Submarines drastically benefit from nuclear as its *extremely* quiet and thus extremely hard to detect. It can also be operated while fully underwater for extended periods, which no other (current) power source can manage. This makes nuclear a massive benefit for submarines.
Carriers, being as massive and critical as they are, also benefit from the near constant operating ability, and the extra training required for operation is minor compared to all the other staffing costs. Carriers still need to carry a ton of fuel for the planes they are flying, so not having to *also* carry the fuel for the ship itself ensure the ship has enough space for other needs. These ships also need a ton of power for both propulsion and aircraft launch catapults, with other systems often requiring significant amounts as well as the carriers are typically the main command hub of a navy.
On smaller surface ships, its just not worth the costs. The US did operate a number of [nuclear cruisers](https://en.wikipedia.org/wiki/Nuclear-powered_cruisers_of_the_United_States_Navy) from 1961 until 1998. There are, however, still a couple of [nuclear icebreakers](https://en.wikipedia.org/wiki/Nuclear-powered_icebreaker#List_of_nuclear-powered_icebreakers) in operation, which are basically a civilian cruiser – all such ships are currently operated by Russia.
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