The ship has sailed on this term of art, but as a native English speaker, I agree with you that it's ungrammatical. I would use a hyphen, though: "physics-based." This answer agrees with you (and me): https://english.stackexchange.com/a/428679.
Here's one way to think about _why_ it sounds wrong. "Physically based" would mean that "physically" is the answer to the question "How is it based?" To a native English speaker, that question sounds odd. A more natural question is "What is it based on?" To answer that question, you need a noun: "It's based on physics." Hence the construct "physics-based," like "evidence-based medicine" or "merit-based scholarships."
> Truly secure entity just wouldn't have private keys on a server at all.
They don't. They have your encrypted private key, but there's no need to keep that secret. (The decryption key is derived from your password, so the password needs to be strong and secret.)
> Such agency can force PM to modify login process to derive password from submitted form, or to just switch private keys for non-encrypred ones, because the user won't even notice it.
Yes, definitely. It's hard to trust self-updating software (like JavaScript in the browser), particularly if you're concerned about targeted attacks. But creating your own private keys and then entering them in the browser wouldn't help you at all against that sort of attack. You would instead need a different type of client that could be trusted somehow not to leak your private key.
It's not uncommon for services like this to offer a downloadable version of the web client so you can pin a version and audit the code as needed. I think maybe https://github.com/ProtonMail/WebClient is that for ProtonMail? If so, you should be able to verify that code and then use that. The fact that an encrypted copy of your private key will live on ProtonMail's servers shouldn't bother you.
That experiment shows that whatever is stored on ProtonMail's servers plus your password is sufficient to decrypt your emails. This could be explained by the private key being derived from or encrypted with your password. ProtonMail's documentation says it's the latter (https://protonmail.com/support/knowledge-base/how-is-the-pri...):
> Your ProtonMail private key is generated in your browser. Before sending the private key to the server for storage, we encrypt it with your password (or mailbox password if you use two-password mode). This ensures that you and only you can use your private key.
Of course, there are other threats to worry about, such as ProtonMail changing their client-side JavaScript to exfiltrate your password. But the system as they've documented it does not appear to have any way to decrypt your email server-side short of guessing your password.