Exactly. Accepting that Kirk's ship in TOS is a relic out of her historical context just adds a nice new dimension to the show, and to Trek in general. Imagine a slightly more diverse Earth, with our Horatio Hornblower commanding a pre-dreadnought-era protected cruiser in WWII, only refitted with oil-burning boilers and turbines, that newfangled radar thing, and (after the first couple of adventures) a pair of choppers in place of Y Turret.
If not for the visuals of "The Cage", cutely reinforced in DSC, it would be easy to accept NCC-1701 as a late example of the NCC-1000 class, in TOS recently refitted with more compact cylinder engines on simpler, straighter pylons for her final sortie under young Kirk, launched into the unknown so that more modern ships could go toe to toe on Klingons closer to home. The general aesthetic would be there, the lineage from ENT cylinder engines through to the TOS ones impeccable, the Box Nacelle Era heralding the Art Deco Nacelle era of two timelines, and everybody being in awe of the heroes who dare sail out in a bucket of bolts that ought to be hauled away as garbage.
Timo Saloniemi