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 thought it was all a bit confusing - it was introduced with no explanation, which felt like it was setting up some big reveal that never came.
I like the, as you say, Giger-esque design but felt it was such a departure that they may as well have introduced a new species.
it seems like the kind of thing that's obviously an out of universe design choice. it's like asking for a lore reason why the male Enterprise crew members stopped wearing eyeshadow after Kirk's five year mission.
I'll never understand why it's treated by some people as some ridiculous expectation that things that couldn't change so drastically over the course of 5-10 years (the entire biology of a species, for example) shouldn't do so, and that we're the odd ones for saying "but wait how is this supposed to take place in the same timeline?"
I just think it points to a failure of imagination more than anything else.
...That's literally what happens in the Dune books.
Hmm yes a very apt comparison, and not at all a complete strawman.
I mean, I can IMAGINE plenty of workarounds, the problem is that even the most practical way to explain them is illogical. It made far more sense that the NCC-1701 looked like how it did in the Cage (2254) up until sometime after Where No Man Has Gone Before (2265), before getting a refit for how it looks the rest of TOS (and again for the movies). Now, if I'm supposed to take the show at it's word, the ship went through a massive, complete refit by 3 years later in Will You Take My Hand? (2257), only to revert one time to it's 2254 appearance for 2265, and go through another refit by the Corbomite Maneuver (2266)? Is it really a lack of imagination here or is it actually that my imagination thinks about these things and fictional implications?
On the viewer's part or the creator's?
If the former, how far do you take it? Instead of Picard's complicated, diplomatic solutions to complex problems, what if he just used mind control to resolve every conflict? What if they just made the Enterprise's shields invincible to damage so there's never a risk of the ship getting damaged? The show has to exist within a framework of rules and 'truths,' for lack of a better word, or everything becomes meaningless because nothing matters and there are no stakes.
If the latter, I'd have to agree. It has to be difficult to jump into a franchise with so much history, but it feels like they changed the Klingons just so they could put their own "stamp" on the show. What reason is there to change them in the first place? Humans and Vulcans still look the same.