No, Berman was the right choice at the right time. But he probably should have left when DS9 ended and talks of a prequel series began. And its not because the prequel series was ENT, since I remember that there was an idea for an Excelsior series starring Sulu that was floating around the same time too.
Berman was heavily based in the 24th century for Star Trek, and telling a prequel Trek story in the 22nd century or late 23rd/early 24th required a new pair of eyes and a fresh set of ideas, not someone that was stuck in their ways. Not to mention the lingering and, at times, annoying issues relating to continuity when producing a prequel show.
Plus, if the studios only care that the product is of good quality and only get involved because they think their ideas would make the show better, then what does that say about UPN involvement in VOY and ENT? Did they not think that what was being produced or the ideas being thrown around weren’t good, thus necessitating their interference?
Something else I noticed about the Berman era… the show themes get more subdued and soothing the further along the Berman era progressed (DS9, VOY, Archer’s theme for ENT). They are a far cry from the TOS and TNG themes which are more vibrant and upbeat, and clearly have an energy behind them. That energy from TOS & TNG is something that DIS had managed to replicate for its theme. One of the few very good things that DIS has done. Music in Trek started to sound the same for the most part during the Berman era. It was mistake to get rid of Ron Jones.
As for the attitudes towards women - Roddenberry era had miniskirts, Berman era had catsuits and decon chambers, Abrams era had women standing in their underwear for no reason. Kurtzman era seems to be the only one that different…so far (unless I’ve missed something). Berman should have definitely treated Farrell better though, and should have had her come back for the mirror universe episode in S7, or for that DS9-VOY crossover than never happened.
LGBT, yes there should have been greater efforts during the Berman era to have at least one character. When the lead of one of your show’s presses for one, and thinks there will be such a character in the next series and it doesn’t happen, that’s on you and no one else.
ENT having a heteronormative crew both was and was not a sign of the times; the culture at the time was getting more conservative all while LGBT characters were featured on major tv hits. If there were LGBT crewmembers on the Enterprise, then they were:
1) Among the 8-9 crewman that left the NX-01 before the Xindi mission
or
2) Among the 27 crewman that died during the Xindi mission

leaving a hetero crew by the time of "Bound".
Then there’s the case of Ensign Massaro, due to that one time T’Pol referred to Massaro as a “her” instead of the usual “him” in S3. Which, if overlooked as a mistake, then in canon it suggests that either:
a) That reference was about a potential wife of Massaro
b) That reference was about a potential sister/cousin/other relative of Massaro
c) That reference was about Massaro, meaning Massaro was genderfluid
And considering the general lack of development of both the character and that character’s personal life, and what happens to the Massaro character at the end of ENT, that was not the best representation of a genderfluid character, if Massaro was supposed to be one at all. So, the Berman era was a failure in regards to serious LGBT representation.
Overall, Berman was good for Trek in the 90s, but should have handed the reigns to someone new in the early ‘00s who could adapt to the shifting tv culture.