I understand why universities would get the benefit of the doubt, but I am not sure having search engines be a government service would be a very good idea.
But let's take another example: Google going into the space of deep learning based health diagnostics. Why does Google need to have access to our medical data when they can sell their solutions as hardware and software to hospitals? Even if they have to use our data for testing purposes, they could sign an NDA so the use of our data would be severly restricted and they would not own our data.
And for many other services, owning our data should not be the default, and even the necessity of seeing our data should be questioned.
I believe that we have fundamental issues with personal data ownership in the web for two reasons:
1. People do not believe web is real life. In the physical world, it is very easy to see how your rights are violated. If there's a person following you for days (when you shop, when you buy your medicine, when you talk to friends), you call the police. The majority of users have no idea of third party trackers. They have no idea what (or rather how much) information they are emitting at each point in time.
2. People have access to amazing products for "free", and they do not know the price of their data. Imagine if you were given a TV, but you would have to babysit a boring kid 2 hours a day for years. I guess not many would want that TV. Force each company to offer two plans (legally): one free + (ads / tracking), one premium (no ads / no tracking), then see how much people care about their data.
I like this idea but only if you force companies to price the non-free version no higher than the actual monetary value of the data they collect. Otherwise you'll have Gmail's "We'll stop reading your private emails" plan priced at 100,000 a month. I don't want to create a situation where only the ultra wealthy can protect their right to privacy.