No, they didn't. TOS was all Kirk, Spock and McCoy. TNG was almost all Picard and Data. DS9 probably had the most well-rounded out cast of characters of any Trek incarnation. Yeah, you saw Scotty and Sulu and Uhura, but no episode revolved around them. TNG solved that a bit with occasional episodes focusing on someone other than Picard or Data but most episodes revolved around those two.
Actually to Discovery I would add Owo (was so glad she was ok), Detmer, Adira Tal, Gray, Vance, Airiam, Jett Reno, Ash Tyler, Cornwell, Nhan, and Landry all as characters that have had more screen time and development than the average Trek character. Compare pretty much any of those I just mentioned with Uhura in TOS, they have gotten much more development. For an added bonus, STO players get even more development of characters like Landry, Stamets and Lorca
Discovery isn't perfect, but it's good and a new version of Trek and it's finding its audience. Hell, it's what has gotten my wife into Star Trek now and she's watched the Kelvin movies and selected episodes of TNG with me and is loving it all so far. People hated TNG when it first came out because it "wasn't Trek", not the way they remembered it.
Oh, and my only quibble with the finale was Burnham fighting Osyrra and jumping all over the place like her leg was just fine ... and then afterwards going back to limping
Oopsie!