While I definitely like the idea of a series that's just a straightforward return to the same setting as classic Treks (at whatever period in time - before, adjacent, after, etc.), rather than a functionally-ground-up-re-imagining that pays lip-service to all that, I'd say there's a difference between, say, 'a series that takes place after TNG/DS9/Voyager', and 'the Rick Berman era'.
Mainly because I think it's fair to say that a lot of the blame for why that era of Trek fizzled out can be placed squarely at Berman's feet.
For example, this was the person who insisted that on Voyager, the actors playing human characters needed to play their roles with restraint, in order to 'make the alien characters seem more alien'. But at the same time, alien design got more and more muted and bland, to the point where 'people with a bit of latex on their forehead, wearing brown/grey overalls' has become a running gag when people talk about aliens-of-the-week on the likes of Voyager and Enterprise.
Or how on Enterprise, the ship was supposed to be gleaming off-white, similar to the original 1701 - but Berman wanted the ship to be more muted and understated (winding up almost gunmetal in colour), and with rather conservative lighting, supposedly so that the ship 'didn't take the focus away from the characters'. Except we already know Berman's philosophy on characters - and the same 'muted colours, muted lighting' approach was also applied to the interior sets, costumes, etc.
...oh, and this was the person who, right after the great Ron Jones won an award for his work on The Best of Both Worlds, decided to let him go because (and I quote!) "he was doing the kind of scoring that was calling attention to itself."
I think it's not unreasonable to instead give credit for the successes of the 'Berman era' to folks like Michael Piller, Ron Moore, Ira Behr, etc., who were much more responsible for some of the positive directional shifts that gave us some of that period's greatest hits (the big one being Piller and Moore coming on board TNG with Season 3 - and most people agree that Season 3 marked the point where TNG became 'TNG', with many of the cast attributing that to Piller).
Frankly, reading things like Piller's unpublished memoir 'Fade In', interviews with the likes of Moore and design team vets like Drexler and Rich Sternbach, and generally all the frustrations of people working on the shows under Berman (much less so DS9, since he was largely hands-off from the time Voyager began - and it sure shows, doesn't it? ), makes me wonder what we could have, if someone just rounded up all those folks, and let them make the kind of bold, imaginative Trek show that they were trying to make, but for the likes of Berman stifling them. Imagine a Trek run by any combination of Behr, Moore, René Echevarria, ...Bryan Fuller, David Eick, Jane Espensen, Tim Minear - maybe folks who'd clearly be a good fit, like Simon Pegg and Seth MacFarlane, too. Get the likes of Drexler, Sternbach, the Okudas, etc. back on board, and just take all the 'Berman era' shackles off - don't get me started...!!
...but eh, to borrow from another classic sci-fi TV show: "if wishes were horses, we'd all be eating steak".