That's what I think also. (And what I've considered doing, in the past...)
Since, I have a modem-router online 24h/day and can easily buy a cheap
computer, with enough processing power and low energy consumption, just for
that.
And the main reasons I don't do it, it's because there's always the
possibility of having to turn the power off, for some reason, and of having
to access the mailbox away from home - with all the inconvenient, and not
very secure (in my opinion), operations that would force me to do.
Anyway... Since, no one that I trade messages with has a secure mailbox, all
that effort is irrelevant...