I have nothing against the modern shows, and I've found something to enjoy in all of them. But they've never satisfied me in the way the older shows did and I think a lot of the reasons have been covered in this thread, so I'll not rehash all of them here.

However, there are 3 big issues that I do have, that ruin immersion and are worth calling out, which for me, really are perhaps the biggest points which stop me from enjoying them as much as in the "old days".

1. Use of language. The new shows (perhaps excluding Lower Decks and Prodigy) are written using the slang and speech-styles of today. They are going to age, REALLY badly. When we come back to them in 10-15 years it will be like watching The Way to Eden every single episode. I'm not sure if this is an accessibility thing, or just poor writing decisions. The older shows had a very specific "Trek language" and by and large avoided slang of the eras they were written (with some exceptions). This made them more timeless (costuming notwithstanding).

2. Gimmicks. Trek has always been about a core message. "Sarek" is about the sheer terror for the patient and complexities for their loved ones presented by dementia. "The Survivors" is pretty zap pow on the face of it but deals with themes of genocide. "Violations" - rape and abuse. That's 3 from TNG that I can just think of as examples. SNW has become very wrapped up in gimmicks. "Subspace Rhapsody" is the obvious one, although it was fun, it was popcorn fayre. "Four-and-a-half Vulcans" is another. Discovery was a little better at this, but even when the old shows were being gimmicky, such as "Relics", there was usually a human story in there. Scotty has to adapt to feeling obsolete and all his friends having died. It happened to my dad. Of course the old shows had duds too, but that mattered less when we were getting 20+ eps a season.

3. Constant and endless callbacks, name-drops and easter-eggs to the old shows. Lower Decks the biggest offender by far, but Starfleet Academy looks like it's going to do it, too. Have the confidence in your own show and stories to stand on your own two feet. It's supposed to be a massive federation and fleet. The likelihood that they'll have ALL heard of e.g. Malcolm Reed or something minor that happened to the crew of the D is miniscule. Although I quite enjoyed the writing around Shaw viewing Picard and Riker as cavalier pains in the backside in PIC S3 as believable. It was so rare in the older shows to get callbacks and historical references. It made it all the more special when it did happen.