I'm going to be honest, Klingons in the TNG era always felt too goofy to me. They weren't a proud warrior culture so much as borderline clownish space vikings who spent more time getting drunk than actually conquering anything. A redesign and change in how their culture(s) present on screen was welcome for me, and I think Discovery did a great job. I even liked the way they recontextualized the Klingon language, to make it sound more alien and more threataning than the staccato, oft-mispronounced mess that we got in the TNG era.

That said, I also think there was a missed opportunity with them. For a long time, I've had a head canon of the different looks of Klingons throughout all of the eras could be chalked up to these all being distinct peoples from within the Klingon Empire. It stands to reason that over a long enough time scale, an empier spanning multiple stars would start to consider people not originally from their homeworld "Klingon," even if they might be genetically different. I always thought it would be cool if the TOS smooth forehead Klingons were actually just one species that were culturally Klingon, where the Worf-type were another, and the General Chang type was yet another. It would provide a way to smooth over the aeshetic differences with an in-universe explanation that doesn't require any retconning except for a handful of episodes from ENT that die-hards didn't like anyway.

But oh, well. One can dream.

I'm not really a fan of "it only looks overdesigned cause its supposed to be alien to you!" That they did with early Disco klingons and have done so far with SNW's Gorn. That line of thinking works for one off antagonists like V'ger, but these aliens are effectively supposed to be recurring characters and and making them and thier ships big balls of (sometimes asymmetric) noise means they all just start looking uniformly chaotic on top of being hard to replicate and recognize outside watching the show.

Klingons have had two totally consistent design elements from TOS all the way through Into Darkness that DSC didn't incorporate. The first is that the majority are fairly hairy, and the second is that their tech is very industrial and bare-bones looking. I can totally buy Klingon factions that stray from either of those things, such as a group that shaves their heads or has more elaborate tech, but the entire species being that way doesn't work. The facial redesign could have worked, but ultimately the masks were too thick for anyone to emote in and they hindered the acting. Season 2 thinning the masks a bit and adding hair was a huge improvement and showed that the concept could work, but the organic looking tech just doesn't do it for me at all as the predominant look in the empire.

Overall, I get what they were going for, but they lost what little consistent design language the Klingons had and it just did not work for me at all.

Most of this reasoning is irrelevant to me simply because I don't view each show as seperate. I watch DIS s1 and see this Klingons and can't help but think "so what about Kang, Kor, or Koloth? How do they look right now?"

It doesn't matter how cool or scary these new klingons look, they have four nostrils and elongated heads when before they were more like buff humans with ridges. That's irreconcilable to me, regardless of how the actual aesthetic makes me feel when I watch an episode.

Taking it at face value, the Klingons looked like TNG, then they lost ridges, then regained them with even more than we'd ever seen before, then they lose them, then they go back to TNG? That's annoying.

I love the design and aesthetic....just not as klingons. Shoulda been an awesome new race of their own

No.

If STD wanted to do something different, then they should have gone 300 years into the future beyond TNG and done something different.

Since Enterprise I have hated that all the new Trek properties have been prequels. The people who are now responsible for Trek either do not trust themselves enough to come up with original ideas or (more likely) have a significant disdain for the property to begin with and don't want to come up with original ideas, for fear of being taken for someone who might do such a thing (ie: nerds).

Thus they can push the property forward supposedly building on the ideas of others, but in order to foist the appearance of originality on everybody in the face of this, they drastically - and without explanation - alter fundamental aspects of the source material. They do this apparently not imagining there will be a backlash. The inability to imagine a backlash can only come from their own personal dislike for the source material. They either find it so goofy and ridiculous that they can't imagine anyone else would be passionate about it - or (again, more likely) they find themselves so superior to the source material in their own minds that no matter what they do, they are certain it will be seen as an improvement. Even if it isn't seen that way, they don't care, again, because fucking nerds.

Klingons are a thing. Extremely well developed, lots of interesting lore. OK, so these new aliens are more scary. They're more dangerous. They're more like warriors. Fine. Put them on a different planet 300 years in the future and stop shitting on the past. Same thing with their stupid fucking mushroom drive hooked up to tardigrade nipples.

Edit: I feel like I should mention, I like SNW even though it's a prequel. Look what it did: changed an alien species (the Gorn) that we really don't know much about - smart(er)!