It's a great idea except that for one person it's going to cost a lot more than buying an account on FastMail (disclaimer: I work there) or any of the other hosting sites (even before you start start thinking redundancy and backups - we have about 10Tb of disk for every 1Tb of pure email quota, by the time you count search indexes and RAID and 3x replication redundancy - two local one offsite)

For more than one person it can get cheaper, but you're going to be on call to fix it every time it breaks - because those other people aren't going to like waiting until you need it. Have fun with that (and I say this after being paged at 3:30am last night to fix a problem that was only affecting redundency for about 1% of our userbase - no user visible problems - most issues are solved without user visible outages)