There is a previous idea that is marked completed, but it is definitely not complete. https://ideas.powerbi.com/ideas/idea/?ideaid=8ea93e7e-1c53-404a-b149-c21fcc06e398 It is possible to copy a table...
This is extra frustrating because Tables and Matrixes give the full and reasonable set of options - Copy Value vs. Selection vs. Visual. Just need the analgous functionality in the Data View - Copy Value vs. Column vs. Table
