You need it for tax forms, background checks, citizenship queries, sometimes bank information, etc.
So your options are:
1. Store them locally on a computer. Typically on some old windows 7 machine in the corner that hasn't been updated in some time.
2. Store documents physically. Which will either be scanned onto random computers belonging to whoever needs them to be sent through probably insecure mail servers.
Or worse, your boss taking a picture of your form and sending it to people that way, leaving the form on their phone.
3. Some other online storage like whatever M$ is offering
4. Use google and somehow store SS#'s somewhere less secure, or obfuscate them in a way no one but a few people will understand and hope they don't block any other files you upload.
Businesses have been deciding how to manage these things since the start that work best for them. Having google force you into procedures that might not work for your use case is annoying at best. And they obviously don't know best if they have issues like in OP's post.
It's like they take away your gun so you can't shoot yourself in the foot, then fires it at things it thinks are problems hoping not to hit your feet.
And what's a few toes to a company the size of google?