Nope, the password is what people type in. They may type the same things at many websites. We should not care what that exactly is.

Why would you want to see actual user password if you can just not see it?

If you see a password you can leak it by screwing up in numbers of ways. If you never see a password you just can't leak it.

E.g. Twitter recently discovered that they were storing passwords in plaintext in logs, GitHub had similar issue.

Take a look here: https://arstechnica.com/information-technology/2018/05/twitt....

Of course, a hash that you will receive from client should be treated as a normal password including all good practices.

No, the password is whatever you send over the wire. If a website processes your attempt to type "password" into "5f4dcc3b5aa765d61d8327deb882cf99" before sending that to the server, then your password for that website is 5f4dcc3b5aa765d61d8327deb882cf99. That's what the server sees and how it recognizes you. The only effect of this is to make it less likely that the user knows his own password.

If user password is "passsword" he may be reusing it across 50 other websites. If you leak information that "password" is linked to "email@gmail.com" I can hack the 50 other websites. If you never knew that the user password is "password" you can not leak it and I can not use it to log in into 50 other websites. Leaking "5f4dcc3b5aa765d61d8327deb882cf99" is useless to hackers, because he cant go and use it to login into another website.

So, there are properties that differentiate "password" and "5f4dcc3b5aa765d61d8327deb882cf99", even if for the server it's all the same.

The distinction you're trying to draw vanishes as soon as this becomes a standard practice. Passwords are already stored hashed and salted. They get compromised anyway, because the data is valuable. Under the circumstances you describe, cracking 5f4dcc3b5aa765d61d8327deb882cf99 (which takes less than a second) is just as valuable as cracking a password database entry is now, because the underlying issue -- reuse of credentials -- hasn't gone away. (In fact, you're encouraging it, so it's probably somewhat worse.) As long as people are reusing credentials across multiple websites, those credentials will have value greater than that associated with their use on any particular site, and other people will put in the effort to crack them. Even when you're generating and submitting a cryptographically secure salted hash, you haven't improved on the situation now, where databases store a secure salted hash of the password.