Google's argument is that they aren't different services, they are all 'just Google'. Say what you want about that philosophy, but it has worked well for many people, myself included.
Identity across Google's services is an absolute mess. They seem to be trying to integrate on one identity per person rather than separate YouTube, GMail, Google Search, Play, etc. accounts. Which makes perfect sense, considering they're all part of the same organization.
"I just want to register for courses, but my university wants me to make a .edu email address!" would be a better analogy. They aren't part of the same functionality, but the organization is moving towards one identity provider across all its services.
Could you imagine the nightmare for IT if email, library, VPN, course registration, brusar, Blackboard, facilities ticketing, software discounts, help desk, file server, 802.11X, workstation login, etc. were all separate usernames/passwords? There is a reason most universities have one central authentication service. My school's network IDs are even even integrated with ID cards so (as of next year) you can reserve space with your network login and then tap/swipe your ID to access it.
It isn't like Twitter asking you to open a bank account because Twitter doesn't also provide banking.
I want to post a tweet but Twitter wants me to create a Profile!