Do they wanna prevent spam? Use SimpleLogin/addy and never give out their actual email. Google knowing it is probably not mean more spam, but you could still filter out emails to the base email address.
Wanna prevent hacking attempts? Enable 2FA, and again, Google knowing probably doesn’t increase the attack surface area too much.
There are a bunch of reasons why you’d want to hide an email account, but the remediations are all very different depending on that reason. At the end of the scale you’d probably never wanna use the app at all, and just login via browser (not chrome), but even then is Google key logging Android? Who knows.
So you’re right, it’s not important why they want to do it, it’s crucial if they actually want to be helped properly.
Look people have a very “all or nothing” approach that I myself disagree with. They want true privacy? Buy a dumb phone, never go online, and disconnect the landline.
I hear you, I also started out with just proton, but I’ve gone deeper slowly — I do have Pihole, I don’t use Google services, but these are not things you need to do to get more privacy.
I think from your comments it seems like you’re just worried Google will know your email address, and that’s… not a big deal?.You probably will give out that email address anyway, so they’ll find it eventually.
The contents of the emails, which is where important data really is, are encrypted in proton. Google shouldn’t be able to read your screen contents, but who knows for sure. So you should be fine for now, don’t worry about logging in the phone.