I think two accounts is pretty common even outside geekdom. Lots of non-techies have gmail as their personal email (even my parents do). And lots of companies and schools are using Google apps for business email.
The intersection of the two must include a reasonable number of non-techies...
Agree with the rest of your point too, it is really strange that you literally can't get support on google products, even if you pay for them as a business.
My mother's school system just switched to Google Apps. Some ensuing confusion -- amongst other things, with Google's/Gmail's repeated GUI rearrangements, she'd lost track of and forgotten about the sign-out command in her personal Gmail account.
I've similarly watched and helped her and others struggle with unintuitive controls e.g. in Google Calendar.
Google may worry tons "about a shade of blue". But their real user experience seems to depend upon individual projects and perhaps individuals. The original search results page and early Gmail were high points. Some other items have languished or declined under counter-productive development.
The intersection of the two must include a reasonable number of non-techies...
Agree with the rest of your point too, it is really strange that you literally can't get support on google products, even if you pay for them as a business.