I think certificates should be like badges that you can collect – the more badges the higher the trust. So if you are a French company, maybe the tax office in France can sign your certificate to show that you indeed is a real company. If you are accepting card payments – Visa and Mastercard could sign your certificate. If you have a domain the TLD owner could sign your certificate to show that it's indeed your domain… And so on…

And then the browser could present these badges in a nice way to the user.