The show has definitely gotten better. Just recently finished Season 3 and starting Season 4. I'm really enjoying the story arc of Discovery time-travelling 900 years into their future. Very interesting perspective, with a very different kind of Federation and Starfleet.
But I still really think the "spore drive" is a joke. It's more fantasy than sci-fi. They really need to drop this spore drive junk. Also don't like the new character, Adira. She's like a Wesley Crusher--but worse, and far more annoying. Good thing we can easily skip stuff now with streaming as opposed the days of TNG when I mostly had no choice but to watch the dumb Wesley Crusher scenes.
Love the upgraded ship though. I like that they changed Captain Burnam's hairstyle and gave her a new "perspective" on things.
However, if you want a show that is closer in style and vision to TOS or TNG...try watching The Orville!
UPDATE: 08-08-2022:
Just finished season 4 and the last 2 episodes definitely makes up for all the shortcomings that came before. Things are looking up: they shipped that annoying Gray character off to Trill. Adira is less annoying without Gray. The spore drive went kaput! Hope it never gets fixed! lol
And finally....I LOVE NON-HUMANOID ALIENS! Far too many aliens on Star Trek or other sci-fi shows are Humanoid or humanoid-like. Yes, I know it's partly a practical & budget matter, and to make it easier to connect with audiences, but sometimes aliens should just be...you know...ALIENS. As in completely different! The gas giant dwellers made for awesome Aliens! Their language was completely different and cannot be translated by the Universal translator (fantastic!), their biology, etc was so so very ALIEN as well! This is what aliens should be!
UPDATE MAY 2024:
Love the Season 5 connection to TNG (The Progenitors). Fantastic treasure hunt. But alas they also fall victim to a typical TV tactic of making something simple over complicated. There was no reason at all to handle L'ak & Moll with kid gloves. Or one hand tied behind your back. Moll wasn't even restrained in sickbay...even after her escaoe attempt! And if you really don't want something potentially very powerful and dangerous to fall into the wrong hands...you destroy it or destroy the clues that lead to it!
UPDATE JUNE 2024:
SOOOOOOO frustrated with Burnam's kid glove treatment of a clearly insane and dangerous person (Moll)! 95% of the problems this season is coz the writers have gone lazy and too woke and they have Burnam being oh so nice to Moll...no restraints on the ship, gives her a dermal regenerator when she was bleeding (with Moll having a weapon out already), telling her the secret phrase to unlock the final puzzle of the Progenitor's tech...ridiculous!!!! I have had to pause the final episode several times just to take a break from the ridiculousness of it all!!!!
They had a GREAT idea for this season, but they MESSED UP the execution SOOOOO BAD!!!! Too woke, too soft on the villains, trying to save the one/few at the risk of the many, total stupidity sometimes! I am glad it's done!
You want REAL STAR TREK, watch Strange New Worlds -- now that is a MODERNIZED version of Star Trek DONE RIGHT!!!