Steering this back to Star Trek...
Regardless of the approach TNG took, I think you can have characters specific a series and characters from other series co-exist at the same time.
Burnham, Saru, Tilly, Stamets, Culber, Tyler, L'Rell, Cornwell, Georgiou, Leland, Kol, T'Kuvma, Reno, etc., etc., etc. are all DSC original characters. People blow the appearance of TOS characters in DSC's first two seasons way out of proportion. Sarek and Amanda aren't main characters. Mudd made a grand total of two appearances in the series proper. You can make a stronger case for Pike, Number One, and Spock. But Pike and Number One barely showed up in TOS, so DSC was making use characters with potential that was never tapped into. With Spock, they put him in a spot that was sufficiently different enough from where he was in TOS, so they could tell a new story with him.
I think the DSC character composition is enough to withstand the presence of TOS characters showing up. With TNG taking place 100 years after TOS, it wouldn't make sense for anyone from TOS to show up. With DSC having previously been set 10 years before TOS, it made more sense for TOS characters to appear in DSC than it ever did for them to appear in TNG.
Also, there was a change in mentality in Star Trek over time. I became a fan in 1991 and I remember that Star Trek was distinctly TOS and TNG. Having Spock make an appearance in TNG was a big deal because they were so segregated. After that, TNG became more comfortable with TOS. DS9 and VOY spun-off from TNG. So, instead of there being two series that were kept as separate from each other as possible, you had four series that were forming something larger instead of being two smaller, separate things. ENT, DSC's first two seasons, and PIC kept moving in the inter-connected direction Star Trek in general moved in after 1991. DSC's third season is the first time Star Trek's 1987 mentality might come back, since we're now going to be once again separated from everything else that was ever made before.
EDIT: Before someone mentions it: yes, I know Burnham was introduced as being Spock's foster-sister. Her Vulcan upbringing becomes less relevant after the first two episodes except when she's interacting with Sarek, Amanda, and Spock. They also re-framed Burnham's character toward the end of the second season.
Now that she knows what really happened to her parents, she's a character whose mother was displaced through time and space who briefly reconnected with her mother before losing her again and now she's in a time and place her mother kept being pulled back to. Or, since she won't be at Terralysium like she thought, she'll be trying to get back to the place her mother kept being pulled back to. Her story is now one about loss and getting to a destination that has nothing to do with Spock or his family whatsoever.
If Michelle Paradise has control of the show for the entire season, she has a chance to remake the show in her own image. Season 3 is when I think the definitive version of Discovery will be established. We'll have one consistent vision and no ties to another series.
PIC, on the other hand, looks like a pure TNG/VOY sequel. And by design it's meant to appeal squarely to fans of '90s Trek. They want to rope in the TNG crowd.
When DSC started, it was off the heels of the Kelvin Films, so the TOS elements there made sense. They wanted people who were paying for the service to be excited about it, so they were hoping having TOS stuff would get potential subscribers more interested. Now they're moving on to doing the same with TNG. The bottom line for CBSAA is to bring in as many subscribers as possible. And they'll do whatever they can to rope in Star Trek fans in order to get them to want to watch. TNG didn't have to worry about roping in subscribers. DSC and PIC do.
