I am the kind of person who enjoys "big weird" scifi like Stanisław Lem. Stories about trying to relate to and find common ground with something so alien that the prospect of even understanding is basically hopeless. Star Trek usually doesn't do stories that, which makes sense as it often uses alien races as allegories or stand-ins for real-world human relations.
That said- I thought those early Klingons were super weird and scary because they were just so alien. It really made sense thinking about how it took a century before they could get to the events of Star Trek VI, and it made the Khittomer accords feel like so much more of an accomplishment. Like- you made a treaty with WHAT?
And just aesthetically their ships and armor looked like something out of HP Lovecraft or HR Geiger:
This is not to say I dislike how Klingons were portrayed previously, kinda like Mongols in TOS or Vikings in DS9, just that they never felt scary to me. They never felt like warriors. I was never afraid for the gallant crew of the Enterprise D (a science and exploration vessel) going into battle against Klingons. But I really enjoyed the alien-ness Disco tried to go with. Anyone else with me?
EDIT: PEOPLE I SAID WHO'S WITH ME NOT WHO ISN'T CM'ON 
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)!
This is the correct take. DSC should've taken place in the future, it was screaming to, but they thought they were better than Trek and could do whatever they want.