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 
How many other Science Fiction properties out there sprung out of a low budget TV show from the 60s but are still producing content in the same continuity without some kind of explicit reboot?
Star Wars is the classic comparison in all sorts of ways, and for better or worse Star Wars avoids this problem entirely by 1) having a much higher budget relative to the number of sets and costumes required for it's initial installment, 2) having picked an aesthetic that is crude, gritty, and seemingly practical which escapes looking dated many years after the fact, and 3) not being set in our future where the advances of modern tech make obviously retro elements look ridiculous.
There is Doctor Who, and that's it.
Actually, DW is a good example, because the continuity of that show is a mess, and very intentionally so. That show thrives in its inconsistencies. There are three different explanations for why the Doctor can change faces when he dies, for example. And each one contradicts the others. There is also no beta canon, every tie in is considered canon. So the doctor has officially met Batman, Gandalf and Picard. That's canon.
In the end IP is a playground and continuity should enhance story. Nobody gains anything from lore for the sense of lore. What does the Klingons always looking a certain way say? Not all that much. It's a nice to have, because it allows you to recognise them quickly and make connections. But if the look is constricting for the creative team, then they should be able to change it.
I mean... not that much. Daleks have gone through three redesigns just since the show went back. Sontarans went from the world's most unconvincing rubber masks to makeup. And how many eyes do Silurians have-- two, or three?
The point is though that DW confirms again and again that how things looked is accurate. We see a 70s Cyberman helmet in 2005, before we see the Modern Cyberman. We've seen the Dalek redesigns happen, and past designs all the way back to the 60s reappear.
Sontarans are a clone race, so its not difficult to imagine changes happened to their process or gene template over time. Perhaps one day we'll see a mixed Sontaran fleet with the short stocky guys from Series 4 and the taller ones from Classic Who and Chibnal. Perhaps Silurians have different subspecies. Those are easy, one sentence explanations, that don't rely on scoffing at old SFX and going "well its broken already anyways".
Doctor Who has faithfully recreated sets, props, and costumes from as far back as the 60s as recently as 2017. Continuity is a different story - there's literally no doctor who canon - as the constant time traveling impacts things. Even the smaller TARDIS exterior from the Classic series is referenced as an actual, visual difference by the revival series. The current powers that run Star Trek would just pretend it was always that big.
I'll never accept the idea that it's okay to update a design but not properly reboot it and set it in a completely different and seperate continuity just because what you're making a spin-off of is old enough that it doesn't deserve to be treated legitimately. How many more years before the crude, gritty aesthetic of Star Wars suffers the same fate as the crude and campy aesthetic of Star Trek?
Whole series of television shouldn't be ignored by their own spinoffs just because their set designer and marketing teams decided something was lame or uncool.
People complained about exactly that during the Prequel Trilogy.
To give credit where it's due, RotS and many of the Disney-era Star Wars products have gone a long way to fitting the glamorous, shiny prequel aesthetic into the gritty, used, "lived in" aesthetic of the OT. I'm not the biggest fan of The Last Jedi, but I actually think the implicication of the shiny galaxy just being a property of the rich inner rim planets was a great move in unifying everything.
There's also the idea that the Empire mass produced everything to a cheaper quality which lead to less frills and faster decay. Supposedly The Acolyte show is gonna extrapolate from this further, and is set like 300 years before the prequels.