I'm not saying the data should never be shared. Often times you can contact the author of a particular study and they will provide anonymized data. Most of the time people don't ask, and to take the time to prepare data for public release would offer little to no benefit.
I do believe there should be "first rights" to publish on data collected with funding from public sources. As for an exact policy by which it could be handled, I don't have one in mind. When you spend dozens of hours writing grant proposals only to have most of them turned down, it would be a sucky situation to have to make the data available for everyone before you have gotten a single paper out of it.
> If others use the data they should put the originators on the data as coauthors on the resulting papers.
It may vary by field, but generating the data alone is almost certainly not sufficient for co-authorship. [1]
[1] http://www.icmje.org/recommendations/browse/roles-and-respon...
Another consideration is the amount of data. Sometimes you're talking about dozens or hundreds of gigabytes of data. Start multiplying this by the scale of universities and you come up with a large expense to store massive amounts of data most of which will be downloaded no more than a couple times. On top of that, the data must be cleaned and made anonymous, and if they make a mistake in the process, there could be large liability issues. See AOL https://en.wikipedia.org/wiki/AOL_search_data_leak