Probably because there is a struggle of accepting that there isn't a "happily ever after." Problems being solved less nearly , and that their are actual consequences that are not as nice as perhaps one would guess.It's not a matter of darkness so much as it cuts against the grain of expectation.
What I think is highlighted best is the idea the idea that Star Trek has never had violence like Picard or DSC. While demonstrably not true it speaks this idea that Trek was more sanitized, and shielded itself from harsher realities. Picard looks straight in to very harsh consequences. For some, that is very unsettling in escapist entertainment.
One of the big issues:
TOS - Was NOT designed or envisioned as directly 'family friendly' viewing. They weren't going to go out of their way to make it really 'adult'; but with many of the topics, it was never designed as a 'family/primarily kids' show. They wanted to do adult themes for the time; and they did.
As time went on TOS became (because issues changed and some of the topics it had dealt with had been resolved and weren't seen as 'edgy' any longer), and Star Trek was molded to be more geared to the whole family as time went on to the point that TNG overall became very 'family friendly' and Rick Berman took more of the reigns from Gene Roddenberry as GR got older.
Now DS9 and ENT tried to get back to doing 'edgier' stuff; while VOY was in UPN's/Paramount's more 'family friendly' vision (again as time went on, VOY had a really interesting premise that was all but abandoned 3 episodes in.
But my point: TNG became the epitome of 'family friendly' Star Trek; and overall, I think MANY TNG fans hoped Picard would try to maintain that because yes, while we're in 2020 - this series still has a very family friendly and forthright character in 'Jean-Luc Picard'; and many wanted that one character aspect to continue into whatever situation the character found himself in.
^^^
The problem for them is: Patrick Stewart DIDN'T. He didn't want to reprise late 1980's/early 1990's Picard in any way. He wanted to make a statement with this show and show a side of the Picard character no one had seen; and there's many a TNG fan who heard this from him, but it either didn't register, or they somehow thought: "No, the circumstances may be dire but Picard is Picard..." - and in a way, that's EXACTLY what the show is to a degree, but because of the situation, it's showing full force how flawed and unreal (even in the 24th century) Picard's view was; and that Picard is now realizing the Federation was NEVER as good/grand/altruistic as he believed; and further that his actions in the past years and his own unwillingness to compromise never helped the situation...
^^^
And some fans who LOVED that aspect of Picard's character (that he's always 'right' and never compromises on a single moral principle -- Which is probably HOW the character became so popular with the "Conservative Right" in the U.S. and abroad; but that's a whole other discussion for a different area of this BBS

) can't cope with that revelation as presented in this series - thus the cries of: "ST: Picard is too dark, and NOT STAR TREK!"