> However, I don't see why you think it would be impossible for most users to set up what I'm describing. If they can install Thunderbird and configure it to retrieve mail from their ISP or GMail or whatever, they could install a two-part system and configure the store part to do the same using exactly the same information.

Then to connect from their mobile they have to open ports on their home networks, get a static IP, know what their IP is to enter it on their phone, worry about a whole host of new security issues.

At that point you may as well run a full mail server.

Many ISPs offer a static IP. This is applicable for small businesses as well, and they almost certainly have one. Anyone with VPN on their router to access anything remotely has a way in.

There are difficulties in running a full mail server far beyond this. For example, many ISPs won't let you run one on anything below a high-level business plan without just blocking port 25 and friends at a firewall. Even if you can, many other mail servers will flag anything you send as likely junk mail if you're not running a well-known mail server yourself. For incoming mail, you need something that's going to be up 24/7/365 if you're going to give it as the MX for your domain, and you need to be constantly monitoring for security issues in real time, because if you're even a few hours late with the patch then you're probably running an open relay already and you just made every blacklist on the Internet.

Basically, if you're not big enough to have your own full time IT department, there are huge practical advantages to sending and receiving your mail via a dedicated SMTP server run by someone who does. These are completely unrelated to the usefulness of having a centralised mail store that can be used from anywhere on your network, or beyond if you provide a way in for remote access.