You are an outlier. For 99% of the users (not an accurate figure, of course) using Android without the Play Store is not viable.
I've used a (company-issued) Sony phone for two years with in a such way, that the only account on the phone was for our Exchange, with built-in E-mail, Calendar, Contacts apps. Granted, the Play Store was not available, Youtube and Maps didn't work, but they were not the reason why I had that phone.