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 
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.
My main issue was less about how they looked and more about what they were capable of. The idea of being able to essentially species change a Klingon into a Human with TOS-era Klingon medical tech sounds impossibly advanced for what the Klingons are known for. Their scientists are few and far between, and even in TNG it's elaborated on that treatments for disabilities aren't even looked into, they just tell you to kill yourself. That doesn't sound like the kind of species that 100 years prior is going to be able to do this insane medical procedure.
The whole deal with that is that they did it, in TOS, without any sort of explanation. We just had that dude, who McCoy discovered was really a Klingon, even though he looked just like a human. That whole thing is just adding an explanation for something that was long-since already there.
Also, you sound like you're talking about the Orions. Do Klingons even have scientists? Somebody has to build the ships!
I liked the way they talked about science from a warrior race in Mass Effect. The Krogans have scientists but they're mostly focused on making bigger bangs and booms. I would probably assume the Klingons are similar.
I know we have a few episodes showing other sides of the castes but generally we only interact with the warrior caste and occasionally see arbiters like in Rules of Engagement (DS9) or Judgement (ENT).
The only time we saw an actual Klingon scientist was in a TNG episode where they had figured out meta-phasic shields or something that allowed shuttles to get closer to a sun than ever before. Crusher was even dealing with some prejudice regarding Klingon scientists and has a few lines about how it feels weird to be working with a Klingon not focused on war and battle.
There was also a Klingon scientist in the Enterprise 2 parter about how the Klingons got smooth heads. He even talked about what it was like being a scientist in a society of warriors.