IMAP solves these problems and is older than the web, by almost a decade. Any mail service of note supports it.
There's no way I could go back to having access to my mail stuck on one machine.
Curious that you should say this, because with webmail, your mail is on the server. With IMAP, it's on the server and on as many clients as you want it to be on.
one that I can access all my mail from any device anywhere in the world
'anywhere in the world'? Good luck reaching your webmail from a place that doesn't have internet connectivity, of which there are a great many places in the world. Or if there's network issues. Offline clients still give you access to email history during network outages.
There's no way I could go back to having access to my mail stuck on one machine.
Curious that you should say this, because with webmail, your mail is on the server. With IMAP, it's on the server and on as many clients as you want it to be on.
one that I can access all my mail from any device anywhere in the world
'anywhere in the world'? Good luck reaching your webmail from a place that doesn't have internet connectivity, of which there are a great many places in the world. Or if there's network issues. Offline clients still give you access to email history during network outages.