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 
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.
That Enterprise arc was clearly intended to apply a (totally unnecessary) in-universe explanation for why Kirk's adversaries were just guys in vaguely asian facial makeup, but there's no reason we have to extrapolate that the Augment virus was a widespread and incurable until the late 23rd century. It could easily have been a relative blip on the radar; aggressively quarantined and/or cured much earlier than anticipated.
The idea that they also needed to make an explicit reference to the augment virus being cured, or explicitly point out "hey, these guys would look less different if they weren't shaving their heads!" strikes me as absurd. These are not difficult conclusions to reach for someone motivated to find them, and there were people mentioning those possibilities pretty much immediately after the first Discovery trailer dropped.
All that needed to be maintained was that the Klingons we see Kirk face in TOS were all afflicted by the virus - while it's still reasonable to assume that, the presence of these hitherto unseen 3rd variant of Klingon complicates instead of simplifies, which is what ENT's arc did. Now what, it's ANOTHER coincidence that THESE klingons are even ridgier than we've seen before, but the other ones are still out there? To borrow your parlance, the Discovery redesign was intended to overwrite and replace what came before, because apparently Star Trek, unlike every other fantasy and science fiction thing I like, is Forbidden from being treated like a secondary world that should have its own internal consistency.
I was completely content to accept it was a coincidence that Kirk only saw augment virus-impacted Klingons in TOS, just like how ST Picard ended up establishing for Romulans (northern vs southern to explain the v shape bone ridge they had through TNG-ENT).
Nonsense-- other long-running universes encounter retcons and visual redesigns all the time. Quick, how old was Dick Grayson when he first became Robin? What color is Superman's S? How old was Magneto during the Holocaust? What happened to Luke's father? Did James Bond fight in World War 2, or participate the Cold War?
As far as I know, those examples all either explicitly exist or are treated as seperate and distinct when you look at their wikis. Comic book continuity sometimes is something the characters are aware of too, so differences are also explained. Crisis on Infinite Earths comes to mind.
Then as someone who does know a lot about this stuff I can tell you that you are making a lot of assumptions that are not the case.
Any example I can think of I have an answer for that solves any sort of continuity issue. Events change because of actual meddling in events and in-universe continuity resets. Events contradict each other between comics and TV and movies because they for all intents and purposes, are as seperate from each other's continuity as Star Wars and Babylon 5.
James Bond, for instance, is a different person from each actor to have played him, in addition to the version from the novels by Ian Fleming. His backstory can change between them, drastically. It doesn't make it in the same category as Discovery Klingons.
That's not canonical, merely a popular theory.