The key to making that happen is disrupting the credit system. Right now scientists aren't incentivized to curate and share their data, so they don't put in the work to do it. You can't put data-sets on your resume, much like you can't put blog posts, or anything that is not a paper. As soon as scientists start getting credit for sharing data-sets, I think we'll start to see it happen.
Similar points apply, as you mention, to instant distribution. Instant distribution will happen more as scientists start getting credit for scientific ideas that they distribute instantly. You are already seeing some disruption to the credit system. In the last 5-10 years, since citation counts have been made publicly available by Google Scholar, citation counts have started to play a much larger role in resource allocation decisions, e.g. decisions by hiring committees and grant committees. I did my PhD at Oxford in philosophy from 2001-2007, and remained involved with some of the hiring decisions at the Oxford philosophy department until 2011, and it's been very interesting to watch the increased influence, over those years, of citation counts in hiring decisions.
Citation counts aren't perfect, but they are another signal. Hiring committees, I have experienced, are desperate for more signals that they can take into account when comparing candidates. Comparing candidates is a tough job. As with any signal, to wield it properly, you need to know its pros and cons. Fundamentally what the community is looking for here is a variety of signals that show how much a highly respected chunk of the scientific community has interacted with a piece of your content, and found it useful.
To get data-sets, and other media, to attract scientific credit, we need to develop metrics that demonstrate the traction that those pieces of media are getting in highly respected parts of the scientific community. I think those metrics will get developed, and that new metrics will play an enormous role in allowing different kinds of media to be shared, and everything to be shared faster.