The thing is, Google Play Services is integrated into the OS. Like Microsoft back then, they've made it so that the OS doesn't work properly without it. For example, notifications won't work. Some background tasks will stop. The battery will last less time. You won't be able to log in to any google app, and some third party ones won't let you log in either. Forget about banking apps. The list keeps going...
I really don't know how Google is allowed to do all this after Microsoft got (rightfully) destroyed in court for doing the same with Internet Explorer.