I think starting a new Star Trek iteration is very difficult. While on the one hand you have a well established brand and universe to draw on, you also have an incredibly knowledgeable fan base, that know the franchise and universe better than you do. There are several hundred episodes to contend with. Fans will recognise (and not forgive you for) repeating a plot line or getting 'technology' wrong.
Dunno about that. Fans are pretty forgiving of the technology gaffs. STV: Final Frontier, Enterprise-A went to the galactic core and back to Earth in less than a year, probably less than a month in universe time. NASA estimates the distance from the galactic core to Earth as over 20,000 lightyears. Voyager, one of the fastest ship in Starfleet at the time, would take 70 years to get from the Delta Quadrant to Earth (70,000 lightyears distance). Obviously Voyager is faster than Enterprise-A. Someone screw up. Most folks didn't notice.
When the Trill were first introduced, they had cranial ridges and no spots (TNG: The Host). In DS9, all the Trills had spots and no cranial ridges. We rolled with it. Gul Macet (TNG: The Wounded) shaved his moustache and called himself Gul Dukat. People noticed, but it didn't bother us. Letek (TNG: The Last Outpost) lost his mean streak and became a bartender on DS9. A few people notice, but again, no harm no foul.
We're pretty forgiving of the little stuff if the storyline is good. If they have good writing, whatever they come up with next should do well. BUT only if the writing is good.
I have to admit that Dr. Bashir as a character rather annoyed the hell out of me. He was insufferably self absorbed; he thought far too highly of himself and was open about it. And the character was very clearly written as desiring a simpering helpless female companion to whom he could play a paternalistic partner. (And of course this is why he failed so miserably with Dax, she was nothing of the sort.) Anyway, I didn't find the character very endearing at all, but he was a good character to have on the station, and as you say he had many good episodes throughout the series.
Oh and Garak. Perhaps my favorite character on DS9...
Well, as a genetically augmented human, he is superior to us. Yes, he was a good character. His interactions with O'Brien is great stuff. Being shot down by Jadzia time and time again, win one for those of us who are inferior. Since she did comment once that Morn (DS9's version Cheer's Norm) was cute. (DS9: Progress)
Garak is a surprisingly well developed character despite being only a minor character. This is why DS9 is my favorite of the series, because the characters come alive.
Chief O'Brien is my favorite character on DS9. He was pretty boring on TNG, just another guy.