And my argument is that the choice of ships there is a compromise, an optimization if you will - not top of the line, not particularly big, exactly because of the risk. Which is pretty much what we see, with other ships being bigger than Kirk's, with ships like Kirk's dropping like flies, etc.
"Ships like Kirk's dropping like flies" - how do you define that? Just watching TOS it would seem almost every Federation ship we encounter or hear about was doomed to be destroyed in the episode (except for the Enterprise, Lexington, Potemkin and Hood). It would appear that your best chance to survive was to be on a ship like Kirk's
Valiant destroyed = not like Kirk's ship ("WNMHGB")
Columbia crashed = not like Kirk's ship ("The Cage")
Archon = not like Kirk's ship ("Return of the Archons")
Antares destroyed = not like Kirk's ship ("Charlie X")
Mudd's Class J Cargo ship destroyed = not like Kirk's ship ("Mudd's Women")
Intrepid destroyed = probably like Kirk's ship ("The Immunity Syndrome")
Valiant destroyed = unknown, 50 years before, probably not like Kirk's ship ("A Taste of Armageddon")
Denevan ship = not like Kirk's ship ("Operation: Annihilate")
Constellation destroyed = a variant like Kirk's ship ("The Doomsday Machine")
Horizon destroyed = not like Kirk's ship ("A Piece of the Action")
Defiant lost = like Kirk's ship ("The Tholian Web")
Automated cargo ship = not like Kirk's ship ("The Ultimate Computer")
Excalibur crew killed = like Kirk's ship ("The Ultimate Computer")
Aurora destroyed = not like Kirk's ship ("The Way to Eden")
Exeter crew loss = like Kirk's ship ("The Omega Glory")
Treating Kirk's ship as one of the biggest and best doesn't seem to offer anything extra IMHO, not with the contrary evidence mounting. An old relic that automatically makes heroes of any people who dare fly one would fit the TOS, DSC and Kelvin bills alike. Plus, you know, in-universe experts are adamant that she should have been hauled away as garbage...
I would argue that Kirk's ship was probably not the biggest
but it was among the best the fleet had at the time. There were probably cruise liners, colony ships, support ships and battleships that were larger in size.
We know that the Enterprise is as fast any ship in the fleet making her uncatchable by others in the fleet ("I, Mudd"). She would still have unbroken speed records in "The Search for Spock". And the Romulans valued the Enterprise enough to
not attack the Enterprise in order to take her whole in order to study her technology ("The Enterprise Incident").
Kirk's line, "risk is our business" spelled out that the Federation and Starfleet had the will to send a range of ships including their best and take the losses and keep on going despite the dangers, IMHO.