Yes, it would. That's the whole point of the Euro currency and the long-term goal of the EU.
And that's the main reason a lot of people thought the quick expansion of the EU towards the east (or even the south) was a mistake - if you have a common market and a common travel area, but wildly differing economies, you create strife.
It's not like they have "spend money on advertising" as a terminal value. They spend money on advertising because advertising makes money.
The problem is that they require a payment method from a country by having residence there, that alone prevents abuse in the overwhelming majority of situations.
For the record, I am one of those cases (technically I'm a resident in three countries, potentially 4 next year), so I'm pretty much aware of the details of it.
I would guess the speed is more limited by 27 governments having to agree on everything.
The largest studios could, in theory, go to the EU with a proposal for how they would like a single market for movies and music to work. They won't because they like the ability to have differentiated prices. Having to sell a movie in Sweden for the same price as in Slovenia translates directly to lost profit. Selling in Slovenia at Swedish prices results in lower sales figures and more piracy. So I doubt the big players are all that interested in help the EU on this one.
So, I just looked up the word "bureaucracy" in a dictionary and it says "a system of government in which most of the important decisions are made by state officials rather than by elected representatives.". I always thought that was what a technocracy was.
The secondary definition is "excessively complicated administrative procedure, seen as characteristic of bureaucracy" which is the only usage I can remember seeing.
Bureaucracy comes from the French word "bureau", that means office. It names the way things are organized in an office, and was created for private offices, only adopted for governments later.
It came into English in the early 19th century, carrying a similarly negative connotation. The connotations have shifted back and forth somewhat since then.
Still, it seems that it's never been primarily used to talk about private offices in English or French; the primary use has always referred to governments.
The problem is that right now the EU isn't one copyright market - each EU country is a separate market, with a tonne of legacy exclusive distribution deals in place. If the EU was a single market, it would be the same size or bigger than the US market and would probably get better attention.
The EU is working on it, it just moves at the speed of bureaucracy (and of course each country has lobbyists in the local media which has those legacy exclusive distribution deals resisting it)
Here's the page on copyright harmonization: https://ec.europa.eu/digital-single-market/en/copyright
And check the "Geo-blocking" and "Intellectual Property Rights Enforcement" headlines here hhttp://ec.europa.eu/growth/single-market/digital/