If I write "ceci n'est pas du français" here for instance it'll remain untagged.
I think the only websites where you can reliably expect the text to be tagged correctly are dictionaries and the like, where it can be done unambiguously and at scale (wiktionary seems to do it for instance: https://en.wiktionary.org/wiki/coin ). In these case it seems like it could genuinely be useful.
I've also looked at a few language learning apps (such as Duolingo) and none of them appear to use the lang attribute at all, even though it seems like it would be a perfect use case for it.
I guess my point is that I'm not sure it's fair to blame a format that strives to be minimalist for having such a shortcoming for lacking such a very specific feature.
Of course if you're a blind linguist you might have a very different opinion on the subject...