Was the 10 day countdown the first time Google mentioned "we'll suspend the account unless..."? Generally on these things - and unless it's an absolute emergency - you'd expect lots of prior warning and at least a couple of "YOUR SERVICES ARE DUE TO BE SUSPENDED" emails in the 48 hours before.
That said, I've rightly called my bank out for sending an email with the subject line "Your account was compromised" - and then the body began "...is what you could be reading if you didn't have adequate security", followed by a sales pitch for some cyber security software. When you get rubbish like this (or absolutely banal "important information regarding" emails) so often, it's hard to know when to bother.