The benefits of OS data are the same as the benefits of OS software. The distinction between "Free" and "Open" is the same as well.
Edit 1: OS data sets are nothing new. The UCI Machine Learning Repository[1] has been around for years. There is also an entire Open Data Stack Exchange site [2], and an Open Data Subreddit [3].
Edit 2: OS data sets are essential for developing new algorithms because they can be used as benchmarks. Nobody should trust a model that's been developed on a proprietary data set for use on anything other than that one data set.
[1]: https://archive.ics.uci.edu/ml/
However, there is a whole bestiary of open source licenses that span the spectrum of "use any way you want" to much more restrictive. But they were mostly thought through for software and data is different; what may prevent proprietary abuse in software may not have any teeth for data.
Unfortunately, Open Source does not help here -- I do not see how OS can be used with data sets. The main OS leverage with software development is that if you use software X to build software Y, X is usually present in some way, shape or form in your deliverable Y. Not so with training data -- once algorithm development is done you can (and usually do) strip training data out and have a finished product that does not require X to run.
Even if one were to require open sourcing derived datasets it is usually easy to segregate the dataset with a tainted (open source) license as you build up your data so the new datasets are not formally "derived" and thus would not need open sourcing.
I would love a better way forward on this, or at least a cleaner explanation of options.