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.