Realistically, we can assume things were always 'slightly' more advanced than they actually appeared to be on screen.
For example, the 'electronic clipboard' props from TOS might look
rather dated in their styling, but we can theorize that in practical function they are at least as advanced as your average Tablet computer. There certainly was no evidence to suggest the contrary.
Everything else we could chalk up as just practical licence.
Around the time of the movies there was a push to suggest that the props, sets, Klingon make-up etc in the movies are how TOS 'really' looked all along. Some of the spin-off media took that to heart.
But later TV shows like DS9 and ENT made it crystal clear that the 1960s era designs *are* canonical. It isn't a case of us making allowances as viewers: in the 'real' Star Trek universe, the ship designs, the uniforms and so on really did go swingin' 60s retro for a few years there in the 23rd century.
So a back-up theory: the Enterprise (and perhaps Starfleet in general) in TOS has got a deliberate
'retro chic' as a part of its design. Starships before and since may have erred more on the side of practicality, but for their own reasons the designers of the then new Constitution Class decided upon this as a statement of intent, or perhaps because it was a fashionable trend.
Likewise a century later, when the Galaxy Class was being designed with that beige color scheme, and things like that wooden horse-shoe as a central fixture on their bridges... just because it was a design asthetic that pleased the powers that be, and made some kind of visual statement to the other galactic powers about how Starfleet wanted to be perceived at the time
If true, it was evidently a passing fad, as later ships like the Intrepid or Sovereign classes went for much more "utilitarian" designs.