For commodity online services, you are lucky that people even give you their email address. The number of people who provide anything more is extremely low. OP is freaking out that they are emailing. If they called him on the phone, he would lose his shit.

The terms of service explicitly state that any communications and legal notices about the services will be delivered via the email address that must be verified at sign up. It is not unreasonable to ask customers to provide a valid way to send them service related messages.

Google isn't going to call you or send you old-school paper mail when they discontinue a service. Even if they did, 99% of people would think that it was a scam.

All that being said, we will always scream test things like EOL of a service just to catch anyone who missed the communications.