I don't think setting the show 50 years before or after its original time would make any difference. It would have been better to plan the show better from the start, probably with different producers at the helm to freshen things up a bit.
Well, they definitely needed to freshen things up a bit and different show runners would have certainly accomplished that, but that’s largely beside the point.
But that “It would have been better to plan the show better from the start” is really the point of the whole thread, since it’s been said that originally, the producers wanted to go much more “primitive” and show a much cruder attempt at early space flight, thus the time frame a century before TOS would have been period appropriate.
But what they ended up with (thanks to “the suits”) was just more of the same Star Trek as usual, so what they
had planned from the start was compromised through no fault of their own -or so the story goes. Given this outcome, revising their time period and setting the series 50 years
later (i.e. 50 years
before TOS)
would have made a difference I think, in that such a time frame would be much more in keeping with the higher level of technical sophistication evidenced in the final product.
As it is, most of the attempts to indicate a less advanced technology were reduced to just changing bits of terminology; phasers became “phase pistols”, photon torpedoes became “photonic torpedoes” and shields became “polarized hull platting” even though they nevertheless weakened incrementally -denoted by percentage points- with each new hit.
An added bonus of the later time period would have been deftly sidestepping many of the continuity errors that resulted, since we actually already knew quite a bit about the level of (relatively crude) spaceflight a century before TOS, but the time period 50 years later is largely a clean slate; so the writers, like their characters, would have been exploring uncharted territory.