But I actually like the idea of it being canon that there's a ship of screw ups roaming the galaxy and getting into very unprofessional scrapes and shenanigans
I preferred the idea someone else came up with, where the adventures of the various generations of USS Enterprise crew were shared by other ships across the fleet, so there were hundreds of ships all having similar adventures all the time - So some Admiral back at Starfleet is just going through different ships logs like "Hmmmm USS Defiant travelled back in time to WW2, USS Musashi had a minor border skirmish with the Romulan's, USS XYZ met a new race of omniscient beings called the Q & USS Voyager had a diplomatic incident with the Iyaaran ambassadors - Ah, same poop different day!" etc etc.
I prefer that notion to the opposite of the Enterprise being the best of the best and having all these adventures whilst the entire rest of StarFleet are just mundanely plodding through space with "adequate" crews, never doing anything worthwhile.