I don't recall it's as popular an opinion that "DS9 is maybe one of the best" though.
Ironically, I think I've heard more criticism around Berman about taking the opposite direction, DS9 being the perfect example: static (it's on a station!), slower paced, dirtier characters (arguably, more complex, but..), and pushing as much as possible Roddenberry's ideals (like, Federation-can-do-no-evil and such). Maybe that wasn't so much Berman at work, I don't know.
Overall, I wouldn't rate DS9 very highly, especially the first season or two, which were downright boring. But I must say, the multi-part story arcs were really cool. Also, poor O'Brien...
I suppose it's worth noting that you can take just about anything from the franchise as a whole. Change, and resistance to change, are both good and bad. There's an episode about nearly anything throughout the history. Really, critiques reflect as much about the critic as the subject. Which is kind of neat, I suppose one could argue all good art should be able to do that?
One thing I didn't like about DS9 and VOY is the character design. They did it right in TNG, each character largely embodying a relatively narrow, caricatured aspect of behavior: duty, adventure, intellect, empathy, intuition, and so on. You could pair a given premise with a given set of characters from TNG, and end up with a different story each time, but the outcomes were much the same between the characters in DS9 and VOY, with more diluted characters, the stories that much more recycled and less memorable.
Anachronism, yeah, that's kind of the problem I think. I mean, the series (and its creator) has its roots in the 60s after all. The stories are often preachy and patronizing. Many of the issues do remain pertinent to this day (sadly, I suppose), but perhaps the storytelling style has changed over time.
Which, bringing things back on topic, I must say the 'Continues' series looks to have captured the spirit of TOS very nicely, yes, down to the corny and kitch. Whether you like the style, for better or worse. Maybe it's not the biggest thing on the whole today (clearly it's not on mainstream television), maybe it's the retro appeal, maybe it's just for the older generation that grew up on TOS. I never really got into TOS myself, but I do appreciate how hard they've worked on this: the design, the characters, the writing, the cinematography, especially with a reduced crew producing it, they've worked hard, and it shows, it's well done.
Tim