[squarefoot]

Not sure if mobile carriers would allow the required ports to be routed, and the connection is usually behind CGNAT, so you can't accept connections from the outside to receive emails. Many home ISPs however can give you a (mostly) unfiltered public IP that once paired with a dynamic DNS service can be reached from the outside. Once the network part is solved, a small cheap box (*Pi like board, mini PC, etc) can be set up to act as mail server, with firewall rules on the router that don't expose anything else to the outside.

[marmaduke]

I meant just in terms of compute power. Like my isp gives me a static IP with forward and reverse dns, and the box lets me put the phone WiFi ip address in the DMZ so all traffic is handled by the phone. Then the termux app lets me run sshd and other stuff.

And actually I think this is a kind of setup people could get into: an Android dist that focuses on self hosting off an older device.