Maybe this question lies more in the realm of philosophy, but if you're using an OS based on AOSP or a browser based on Chromium, are you really google free?
When I get my new phone I will likely attempt to not install google play services, but when I stopped using gmail I switched to Proton, since they offer a wide suite of services. And while Proton Pass and VPN are available outside of the google store, Mail, Drive, and Calendar are not, so unless I can find a way of connecting to those services outside of google, I will likely have to install play services again.