If I was Postmaster General I would like to see a post office ISP that only accepted mail from government departments, local authorities, banks, hospitals, doctors, schools and other agencies. From there people could setup a forwarding address - if people wanted to just check their mail from one account, e.g. gmail, they could have the 'important stuff' rolled into it. Or they could setup POP/IMAP.
There could also be a webmail where you would be able to have highest accessibility standards. Clearly the cryptography would have to be in place so only the sender and the recipient could read the mail - a 'virtual envelope'. Naturally there would be tracking tags so they knew if someone had read that 'final demand'.
As a competitive service for banks etc. wanting to send out statements it could work very nicely. Good for trees, too.