In fairness, regular update and recalibration of the warp scale makes some sense. Otherwise you either end up with warp 465, or warp 9.999999997 which isn't very pithy to say in an emergency. Maybe by the 25th century it's been recalibrated again so now Warp 15 is infinity, or something like that.
I seem to recall that the old warp scale was quadratic - Warp 1 - light speed Warp 2 - 2 x light speed Warp 3 - 2 x 2 x light speed Warp 4 - 2 x 2 x 2 x light speed etc etc
Perhaps they should dispense with numbers for warp factors altogether, and code-name them after animals or colors, or both. Or something else equally arbitrary. "Captain, the hostile is on a direct heading toward the Sol system at warp green platypus." "Pursuit course, ensign. Warp factor pink fluffy bunny!" Kor
Other then the giant obvious prosthetic nose on the Discovery Klingon you can't see the back of the lizard head from a frontal picture which is the other half of the problem.
The novel 'Federation' had a future Enterprise using something called Sidewarp, and the factors were letters - but it's been decades since I read it, so could be misremembering some of it.
This page on Memory Alpha pretty much explains everything, but the truth is, I don't understand it all or even particularly care how the warp scales compare between the eras as long as a scale is used relatively consistently. The concept of a change having happened mostly just exists as a retcon, and knowing that is enough for me.
Sure, and if they're called out as a different subdivision of Klingons that would work for me. But if they're just saying suddenly that all Klingons past and future have always looked like this, then that's where I'd have a problem with it. Whatever you think of the augment Klingon storyline, at least it was an attempt to reconcile the disparity.
As someone mentioned before, they do look recognizable as Klingons from a frontal view. The elongated head in the side view makes them look less so. However, I suppose looking like Klingons from a frontal view is enough for me to say "yeah...Klingons". In fact, the DSC Klingons look more like the last iteration of TV Klingons than the TMP Klingons looked like TOS Klingons. The difference between TMP and TOS Klingons was much greater than the difference between DSC Klingons and, say, the ones seen in TNG. They pretty much had to "tell" us the aliens we saw at the beginning of TMP were Klingons. I think DSC will find a way to do the same (i.e., "tell us" in some subtle way), but I think we may have been able to recognize them as Klingons even if they didn't tell us.
When Star Trek the Motion Picture came out I just imagined that the way the Klingons looked were the way they always should have looked and therefore did look. I didn't need an in-universe explanation like Enterprise gave and I still don't need it. But if they want to say all of these are Klingons I'm cool with it.
Um, just to reign the topic in a little, The Star Trek YouTube page just uploaded footage from the Discovery panel today in 5 parts.