As it is, it is you first post didn't address "why",
Because the "Why" you keep asking for is a personal question about slating your own emotional needs. I can't answer that, nor do I wish to. I'm here merely to discuss the "how".
Frigates do have a considerable number of weaknesses over larger themed fleets. They depend on their numbers, they die faster and they suffer a severe attrition from combat losses. Officers provide inherent buffs that allow ships to succeed, but do not scale in effectiveness with small ships. You'll never have enough officers for a frigate fleet, nor can you buff frigates to overwhelmingly survive battles without shifting the entire scale of the ship or doing other kooky things. Instead, the idea is to support frigates from the back end. Don't depend on them being super powerful, or faster, or stronger, or insanely survivable. Instead, make them more expendable by reducing their attrition on the fleet. The direction for using frigates becomes less of a "can I win with them" and more of a "doesn't cost me much to try". And while it is true that frigates are quick and not expensive to replace in the core worlds, that option simply isn't available in deep space. The only solution is to bring the necessary resources with the fleet.
A capital dock supports frigates by reducing attrition losses. Ships blow up just the same, because battles are dangerous and small ships die. It happens. It should happen. It'd be pretty crazy if it didn't happen. Those losses get recovered and they get healed up faster, therefore a fleet can maintain its frigate strength across multiple battles, instead of being utterly devastated after a handful of encounters.
B-but it's a capital ship! Muh purity of fleet
Yeah so what. The burn speed is perfectly workable in context. It never enters battle, you don't put a prometheus or atlas into battle either. The primary combat still happens with small ships, and the victories/losses depend on them. The only difference is they have a logistic backbone for long lasting support.