Why can't secure email be based on simple https-server? I assume the server would need to store the messages in plain text, or maybe not, but the communication

Why can't secure email be based on simple https-server? I assume the server would need to store the messages in plain text, or maybe not, but the communications to and from the server should be safe with https, no? You would not need to trust such a web-server any more than you currently trust you email provider. But it would be much safer. Why not?