I would think that if one is specifically trying to do something in a franchise set in a specific timeframe, one would at least attempt to make that timeframe look similar to what had come before. If for no other reason than to make it possible to reuse older material without much or any need to explain it away. Also so that the audience can get the when this is taking place relatively easily.
TMP works as a tech upgrade and is explained as such for much of it. The Klingons are different, but flying around in a ship that looks at least recognizably like the ones from the third season of Star Trek. The bridge crew of the Enterprise are played by the same actors, so that connect the dots for the audience.
For TNG, we know going in that it has been roughly a hundred years since TOS, so it is understandable that things change, yet also looks somewhat the same or familiar.
Star Trek (2009) we understand that the timeline is different. Things changed, but somethings are still at least partly the same or at least recognizable.
With Discovery coming, we aren't sure what they are going to do. If they are intent on making this series set about ten years before Kirk's missions as seen in TOS, than it should stand to reason that some of the authentic qualities would remain recognizable even if made to look like a future of 2017 as oppose to 1967. Design elements from Star Trek: Enterprise and/or USS Franklin in Beyond being used for older ships and/or props would also help for consistency. Should a Constitution-class starship, for whatever reason, show up on screen, it should probably look somewhat like the ship from the 1960s and not something radically different. If they have a bridge set for said Constitution, it should probably looks somewhat like the 1964 bridge in pattern and maybe coloration. The details can be series modern 2017-ism. Just the look should be close enough to say, "Oh so that's what it would look like today instead of filmed in 1965", instead of saying "That looks totally different, there is no way that could be the same thing as before" Even taking into account our own technological advances, you don't change something radically when you don't have to do so. Other ships can have any design styling they choose and Starfleet ships could look different than a Constitution both inside and out, but if a Constitution appears on screen, it should look at least plausibly like the old 1960s ship that they kept using all the way up to 2005 and even 2013.
