Long winded admission that you might as well pay for google's email service.
Receive only (e.g. account signup)? Use your own account. Not important anyway? Use your own account. Your recipient needs the email more than you? Use your own account. None of the above? Use a mainstream provider for that email only.
Not to mention I use a separate email per service so I can tell if there's a data breach (usually end up seeing an uptick in spam).
*Edit: Not to mention I can pay for a relay service other than Amazon SES without using Google's services, and for significantly less.