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'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 didn't like the Disco Klingons. It was too much of a change to an established race for me. But, I like your idea and I think I could have been more on board if they had done it that way.