As I understand his argument, it’s “Changing port number add security, therefore it’s a good idea.” I think nobody argues that it adds security . The problem is that: 1. It adds very little security: 16 bits is not much, and the result is not 256 bits (say) of SSH key plus 16 bits equals 272 bits, but instead effectively still 256 bits, or 256+8×10⁻⁷³ bits. 2. The security it adds is itself bad (sent in cleartext, ea…
Yes, if you have a long password or key-only method of logging in, and disable root login, and patch the daemon, then party on.
But for the extra bit of protection against 0-days and bullshit amounts of logs from quick port-22 only scans on your network, it helps to move it to another port. This is why I disagree with your mathematically founded reasoning. It doesn't fit with real world scanner behavior.
If it's just your home network, it's not confusing because only you use it. If it's a corporate network, then using putty might be a little annoying, but it's not hard to communicate another standard.