Sorta. SendGrid lets you point an MX record at them and they will process incoming emails by posting them a webhook. Google App Engine does something similar... but neither option is particularly flexible or can handle emails with large attachments.

Personally, I'd pay for a service that let me point my MX records somewhere, then be able to specify if I wanted a webhook called, or to get the emails pushed to S3, or a message queue... or some combination thereof. I'd still be developing, just not worrying about the mail server interaction itself.

There are lots of "simple services" that make developers jobs easier. Why write my own file storage system when I can use Amazon or Cloud Files?