No.
Cobra Kai is awesome for what it is...because it knows what it is...and that is that Karate Kid was kinda shit, but amazing at the time...but also still shit then.
It's a generational thing.
Basically, if you haven't grown up with Karate Kid and "appreciated" all that those movies are at the appropriate age, then Cobra Kai will just be plain shit (justifiably), and not the delightful, brilliant shlock that it is for those that get it.
....all that being said, for the shit that Karate Kid gets these days, go back at that time and think about what it did for people like Pat Morita, Japanese and other asian actors, Japanese culture at the time. It was actually HUGE. It's grossly unfair to bitch about it as "cultural appropriation!" or embarrassing or any crap like that, because it turned on an entire generation of US kids to that. Karate Kid may have been shit for it, but a lot of kids now started to learn about it on their own...now they are the ones that hate Karate Kid for being shitty, but they never would have gotten to that point without it.
That, and it also did a lot of good for casting real Asian actors in Asian roles.