I do this in my SharePoint responsive design classes. Students are taught how to make a custom table for a list view to include the data-attributes necessary to render field names at different breakpoints as well as data-attributes to set which breakpoints the fields should be visible. It's only one possible solution, as you've found (and others have mentioned), and I do show others (like overflow-x: scroll and such).

Data tables are hard in a corporate setting when mobile access is thrown in. It takes a lot of planning to determine the actual needs of users whose usage context puts them on a mobile phone or a tablet. Mobile <> in motion, and tablet <> on a couch. Oil rig operators may use a tablet to access production data, and so their tables would need larger targets for scrolling or toggling columns, and a larger/heavier font with higher contrast colors to be visible in harsh lighting conditions. Field sales reps may be using their phone while in the lobby before a sales meeting, and don't necessarily need just a subset of data.

Content may be king, but context is its queen.