Your comment reminds me of the infamous Dropbox comment: https://news.ycombinator.com/item?id=9224
I'm sure there are secure websites to do it too. This isn't it though.
The dropbox comment isn't relevant. It's a bias to say "I remember this thing was criticized in a similar way but succeeded" and map that on to "so other criticisms aren't valid".
It's far more often than things seem unlikely to succeed to critics, and then quietly fail than that things seem unlikely to succeed to critics, but then succeed. After all, almost everything ever made doesn't see widespread success.
Our brain does remember the latter cases more, and that leads to the bias.
I see it most commonly with the phrase "X started out small too" as a defence for why something small will grow to something big, when in reality that's cherry picking massively.
Such websites have to be audited every single time you use it. Even if I only have a web browser and nothing else I would combine random.org and diceware.com instead of trusting some website.
Forgive me if I don't trust my password generation on the servers of someone who is either sock-puppeting, or having a friend do something that does not look all that different.
Even if I trust the person who runs the browxy website and servers, I don't trust my password generation to a multi-tenet environment. Browxy is running this code in docker containers on a machine with many other docker containers running arbitrary user-submitted code. The intel vulnerabilities over the past year or so have made it incredibly clear that running sensitive code on the same CPU as totally untrusted and possibly malicious code is a dangerous proposition and there are numerous potential side channels to exfiltrate data.
Trusting password generation to a website that generates passwords on a shared machine is even worse than the usual password generation website which at least uses javascript/securerandom to do it on my CPU.