Currently, digital media is released online at different times by separate providers in each of the 28 EU countries. This allows the creators — the television producers and musicians — to charge prices in line with the demand for their product in each individual country, thereby maximising their profits. When the EU’s Digital Single Market makes this illegal, the profits of TV, film and music producers will plummet.
Geographic price discrimination does indeed allow distributors to augment their profits. (Distribution costs, on the other hand, tend to be flattened when your goods need not be physically shipped around, or placed on an actual shelf in a physical shop.) Which means that somebody is paying for those maximised profits, and customers in higher-priced regions are paying disproportionately, so long as distributors contrive to keep sales in lower-priced regions from becoming sales or resales into higher-priced ones.
There are genuine questions to ask about how a more liberal market in digital goods would affect the distribution of (gross) profits and therefore investment; but those questions include a fair few about who is currently paying higher prices and why. Eurosceptic campaigners (who might have been expected to shower less love upon a regional carve-up by vested interests) should be more careful about letting the E.U. look like the sole champion of the beleaguered customer.