The doubling of post systems as rural bankers in Europe has interested me for a while. Even today the basic bank services in Switzerland are done by the Swiss Post. It makes a fair amount of sense and there are some neat synergies. Even fairly small communities have a post office; postmen visit homes regularly and so can e.g. pay out cash pensions; sending out documents or valuable mail at a post office is intuitively similar to sending out money to pay bills; post has implicit identity systems to make sure mail gets to the right person.
It seems it wouldn't be very hard to adapt post systems to electronic age in most countries. It is basically accepted that electronic banking will verify identity by sending out mail (e.g. with login details) so the post is already involved to an extent.