Fair question. I don't necessarily have something specific in mind, I just have a generally high prior of things like: the law is complicated; DMCA is complicated; things don't necessarily mean what they sound like they'd mean; arguments like "if you allow this you can't possibly forbid that, what on earth are you thinking" are unreliable at best[1].
But the sorts of things I could imagine going wrong with your argument might be...
* Yes, browsers are in violation of the thing bitwize quoted, but it doesn't apply to them for reasons written elsewhere.
* Yes, browsers are actually in violation of DMCA. People probably noticed this when the law was being written, but no one listened to them. If anyone tried to enforce DMCA against browsers, DMCA would get overturned, so no one's going to try. (I think this is unlikely - if there was an argument that browsers violate DMCA, I think I'd probably have heard of it. Probably. But including for completeness.)
* Browsers need Javascript engines for many many reasons. Youtube-dl (afaik) needs a javascript engine specifically to get around this obfuscation. That could be relevant somehow. (Similar reasoning might say that locksmiths are allowed to own lockpicks and no one else is. I believe the law has roundly rejected that. But that doesn't mean the law would reject this, too.)
Again, not claiming any of these actually apply. Just, this sort of thing is why I'm hesitant to make inferences that seem otherwise sensible.
[1] https://xkcd.com/651/