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 
I remain amazed that many people insist that T'Kuvma and company are irreconcilably different from the TNG era portrayals. These are big, carnivorous-looking aliens with prominent forehead ridges and significant individual variation in appearance. They're different in some small details, like the extra nostrils, but outside of the most extreme visually literalist stance, is it really that hard to square these guys against Chang, Martok, and Worf? Replace the shine and detail with a classic rubber mask, silicon makeup, and matte brown body paint in exactly the same head and body shape, stick them at a side table in Quarks circa S6 of DS9, and I challenge you to notice anything amiss.
What this rework did do was make them feel so much more alien, and so much more dangerous. They outright eat people, which was occasionally hinted at but is noted far more literally in Discovery, and very, very easy to believe looking at these guys. I wish they hadn't backpedalled so hard with a return to the 1980s makeup in SNW 2x01, because I would have loved to see these monsters chumming it up with Spock: that scene would immediately have been slightly more unsettling, bringing the audience closer to what Spock and his crew are likely feeling about their momentary drinking buddies, instead of the much more casual feel we got from Klingons who look just like our old friends from DS9. These guys are still dangerous aliens whose friendliness is tenuous and temporary; they would literally eat Spock if circumstances were slightly different. We shouldn't forget that.
For me, having them look like TNG Klingons doesn't even solve the problem because ENT had implied that shouldn't happen until the TOS movie era. They could have rendered explicit the implication that not every Klingon was infected by the virus, but that still doesn't support making the Klingons look how they did in s1 DIS.
Folks forget the klingon's made that Augment virus which then got loose in a lab breach. If they could do that to themselves on accident imagine what they'd do to themselves on purpose to try and compensate as the implications of the augment virus turn thier society upside down. There's much I don't like about Disco Klingons but the face redesign intrigued me as a potential reaction and over correction to the augment arc in ENT, and how past exchanges like that ultimately lead to federation vs klingon hostilities. Unfortunately Disco didn't capitalize on this probably cause if they start explaining things they'd ultimately have to admit they can't get away with haveing the longest heroship in canon...