I work in a "nerdy field" so sometimes I feel out if people are Star Trek fans. A lot of times no or they say they are but after a quick discussion it turns out they are very casual fans compared to people on here. Anyway, my point is when I discuss Trek with them I have found most people have no clue there is a difference between the shows timelines and equally recognize Kirk and Picard. The next most frequent one they know is Janeway or the "woman" captain. Then comes the "black"captain (very few seem to know his name). And no one knows there was Enterprise. Granted this is a very small sample size.
Anyway, my point is that Patrick Stewart resonates in many peoples minds too as Star Trek and to discount that is utterly foolish. There is no need to stick to Kirk as the non-fans don't understand any of it anyway.
You could, of course, turn that argument on it's head by pointing out when TNG aired TOS was trek for
every fan. People complained because it wasn't what they were used to and predicted it would fail because of that. What happened in practise is it came to rival TOS and many of the new fans grew up to become exactly the people you are talking about, those for whom TNG is trek.
Now we are seeing those same complaints about Michael Burnham and Captain Lorca, they aren't Picard, much as Picard wasn't Kirk. Many of the long standing fans will doubtless give this a go, some will like it, some will not, (personally I suspect those who have already adapted to repeated reincarnations may be the most forgiving in that regard) but the series will also attract new fans, fans for whom DSC is trek.
DSC is set in a time period
almost concurrent with TOS, but besides a couple of non crew cast members and some easter eggs that may well be all they have in common. The team working on it will make their own path, using their own crew, their own plots, their own take on the trek universe and thus equating it with a return to TOS based simply on the time period is disingenuous.
DSC might well fail, or it might well be a success, but it should be allowed to fail or succeed on it's own terms, not as a re hash of TOS.