For true freedom of movement/services/goods, the EU would have to be treated in the same way as a single country is treated today. A British subscription doesn’t care what county you are in, and an EU subscription shouldn’t care what EU country you are in.
The problem is that rights holders in non-EU countries don't care what EU law says. The US owner of rights to a TV show may want to sell the French broadcast rights to, say, Canal+ for $x million, and the same rights for Italian broadcasts to, say, Sky Italia, for another $x million, making $2x million in total. If Canal+ comes back & says "EU law doesn't allow that restriction, we have to be able to provide that broadcast to anyone in the single market who asks" the US rights holder can just say "OK, EU population is 7x that of France, you can have EU-wide rights for $7x million", which Canal+ would never accept.
Things obviously get tricky with the language issue. Arguably Canal+ would only require French-language rights, but there are many French speakers in the EU outside of France, and if English-language rights are considered the pool of potential viewers is even bigger, even in countries where English isn't an official language.
It's possible that streaming services will allow suppliers to charge based on actual subscriber numbers, but that's still far from easy to manage, so many non-EU rights holders won't see it as worth the effort when the current model works for them. The EU could just ban them, I suppose, but there might be a sizeable consumer backlash from the many people who don't travel & see the current system as OK. The EU might see this as an idealogical issue, but in purely practical, pragmatic, terms, how many people from the EU actually move countries often enough for it to be a problem for more than a minority of the 450m people in the EU?