Save new password hash in database after login

Question

Could it be a good idea to "re-hash" a password after every login and save the new hash into the database? Are there any pros and cons for this in terms of modern security standards?

Here a minimal code example in PHP:

function login(string $username, string $password): bool {
    // function arguments coming from $_POST
    $user = User::findByUsername($username);
    if($user) {
        if(password_verify($password, $user->password)) {
            // re-hash password ...
            $user->password = password_hash($password, PASSWORD_DEFAULT);
            //  ... and save it in database
            $user->save();
            return true;
        }
    }
    return false;
}

Answer 1

Rehashing the password after each successful login does not increase security.

If the function password_hash() would use a fix global salt, the hash would look exactly the same for the same password. So an attacker would not even notice any difference in the database.

Though, the function password_hash() will generate a long enough unique salt if used properly, and several hashes of the same password with different salts will not make brute-forcing easier.

So while rehashing does not weaken security, it does not help in any way either, it is better to use the time to increase the cost factor.