I probably would never try to implement this on my own website. My login pages don't use JS, so unless the browser did the work for me, it's complexity that I'm never going to understand running on the most crucial page on my site. Moreover, though, users run so much shit in their browsers. More than half of the logged errors on my site are from user scripts and browser extension content scripts doing lord knows what…
It's a problem with PAKEs that they're kind of neat to think about and play with, so people look for things to stick them onto. They're usually not the answer, which is why you don't see them used all that often, and why they're used almost exclusively in custom protocol settings.
(It doesn't help PAKE adoption that most custom protocols are better served by standard authenticated key exchanges based on real cryptographic secrets, rather than passphrases).