[jwr]

No, the padlock means that you are likely connected to the website that the URL bar shows you. This is useful and should not be discarded because of condescending ideas about "average users". It also has the advantage of being easy to explain.

Some people assign additional meaning to the padlock, which should not be done. It doesn't mean you are talking to your bank, it only means that you are talking to the website shown in the URL bar and that reasonable (simple) checks were performed to make sure that is the case.

I'd suggest we invent something better before we start breaking it.