Many people (including me) raised this issue internally at Google more than a decade ago now during the Google+ era. Vic Gundotra decided that not using your "real name" was a bannable offense despite the many legitimate concerns people brought up [1].
This was of course an automatic process and there were (completely predictably) false positives. This would kill your entire Google account, Gmail included.
I was one of many voices who argued that was completely stupid. The worst thing that should happen is a policy violation on a given service should terminate or suspend that service only. It should NEVER kill Gmail. Why? Because the end result is people will ultimately only use their Google account for Gmail.
That's what I have done since and what I recommend everyone else do. Never tie your Google account to any other Google product. You may well regret it.
It's wild to me that this is still the case. The issue isn't large enough for any executive to care. That means the decision will come down to a few stubborn individuals (probably a VP of PM) who are maintaining this position.
There's nothing you can buy from the Google Store that you can't get from Best Buy or Amazon and those will be infinitely more accountable.
[1]: https://www.youtube.com/watch?v=HMqZ2PPOLik