Google wants you to do special things for them. Have you gone to https://postmaster.google.com and set up your domain there?
(I'm hoping I won't have to partake in this.)
So what I'm saying is, no, I don't want to link my domains to my Google account just so that I can send mails to them. And I'm going to hold out hoping that their systems are collecting enough trust in my domains and/or IP addresses in other ways so that it won't be necessary.
I discovered the following for outlook.com: https://postmaster.live.com/snds/index.aspx?wa=wsignin1.0
Are there similar tools for aol.com, yahoo.com and icloud.com? (to basically cover the big 5)