OK, quick 'n dirty opinions on your questions:

• Is this a stupid idea?

Great _idea_, but it's likely to be a nightmare in practice. I just don't want to think about the scope for abuse if the implementation isn't rock solid (even then...)

• What are the pros/cons to this idea?

Pros:
Erm...

Cons:
You suddenly find that your account is being used to spam everyone and their dog.
Update: Who knows what sort of wierdness proxies and oddities in your system will introduce to the situation!
SMTP has been around for a long time, and does the job reasonably well.


• Is there an easier way?

Find a webhost that has shell access and SSH port forwarding available - forward everything over an SSH tunnel to your webhost's SMTP port - send the mail that way.
I actually do this to bypass my ISP's broken mail-relaying and solve a few other headaches in the process.



• Is this a common problem for others?

Not this exact problem, but as mentioned above, I've had hassles with the way my ISP catches all traffic destined for port 25 (mail/SMTP) and tries to relay it for you.

• Any suggestions?

Avoid it if you can.
I'd probably make a great proof-of-concept project, but I wouldn't like to trust it in production or on an internet-exposed site.

Sorry to be so negative, YMMV :-)
I'm actually quite interested to see what code or suggestions everyone else has on this.

BazB