Inverting the "activation email" process

It's fairly common for websites to send an activation email to new users, with a link or code for them to use to confirm that they do in fact own the email address they used to sign up.

This has issues, however. Most commonly, spam filters. And then there's some email providers that don't even have a spam folder, and just silently delete things...

But what if instead, the website requested for you to send an email to them? A handy mailto:activate@example.com?subject=CODE_HERE link can be provided so all a user has to do is hit Send.

This bypasses all the issues of spam filters "eating" the activation email, and the only downside I can really see is that people are used to activation emails so flipping the whole process around could be confusing.

Has anyone done this, or considered this, before? Am I on to something, or should I just stick with what everyone else does, despite its flaws?