That assumes all your navy does is fight pitched ship-to-ship naval battles. Historically, countries also needed ships for important functions such as reconnaissance, communication, blockades, harassment of enemy shipping, protection of friendly shipping, coastal raids, coastal security, transport of troops and supplies, and control of smuggling. In fact, the only reason you even care about winning big pitched naval battles is to control the seas so your navy could execute those functions better than the other navy! So you definitely need all those small and medium-sized ships, and in the case of a big battle, you wouldn't automatically send them away. You'd bring them to the fight as long as you believed their impact would outweigh the risk and trouble of bringing them.

Source: I read a couple of Horatio Hornblower novels a decade ago.