Is it possible to get the list of users / groups a dataset is shared with?

there is a Domo Governance Dataset calld PDP, but that's probably not what you had in mind.  AFIK there is no way to report with 100% certainty what you're asking for, other than to look at which cards have been shared with users (b/c cards are power by datasets).  You can get a hint by looking at the Domo Stats Activity Log but I suspect that's not quite what you had in mind.

I hear you on the clutter issue.

-- Implement content management practices that makes UX / UI the responsibility of the business --

If it's not a data security problem, then maybe you can direct users toward practices that let them get to the stuff they want to see faster.

For example, when I do content management workshops with clients, I show them how to set up a directory of 'important dashboards' or 'important datasets' so they can navigate using a table card with URL links.

On the Content Management side, I recommend clients only build cards against production/dashboard datasets, and minimize access to intermediate and raw datasets, that way users are only likely to get access to 20 or fewer datasets, instead of ALL of the work in progress datasets.  

I also get very aggressively prescriptive about generating datasets based on dashboard and production datasets to minimize dataset growth (as in ... it's not permitted).

-- Embrace Domo's Security model because it minimizes overhead for IT/IS --

I get your point about 'it'd be nice if you could generate a report on which data users have access to'... When I consult customers, I tell them, "unless you explicitly apply PDP assume users will see all your data."

SQL developers are accustomed to controlling data access by limiting access to tables (because that's all that was available by the database engine when we were learning to become DBAs).  While Domo's model is contrary to a SQL dev's instincts, it does make it easier to scale without significantly increasing governance efforts.

Consider your desired alternative, if you secured data on a dataset level AND a row-level, that's three actions every time you want to share a card with a user instead of just one (share dataset, set PDP, share card) versus just (share card and or PDP).  Now imagine you're managing content for thousands of users.  Maybe this is why BI/Infosec operates at a slower pace than the business typically desires!! 

If you're on the BI/Infosec side, it sounds like I'm slinging shade, but actually, having been there, I'm on your side!  Your job just got easier!!  All you have to do is configure PDP when required.

-- An easier approach --

The responsibility for content management goes back to the business... where it belongs!  UI and UX are a USER problem.  If they don't like how cluttered the data center is, don't go there!  Use tools for end-users (cards and pages and well-designed dashboards) for navigation. 

Of course ... if your BI/Infosec team are frustrated by how many datasets are being generated... build content management and development frameworks that minimize dataset proliferation!  Use tags for filtering, and leverage the governance datasets to track the spawning of datasets, and refactor. refactor. refactor.