Unfortunately, that isn't really what happens in practice. Although many states share the same currency, they do not share the same wealth or cost of living. You can't just pick one price for your product or service in Euro and then expect that everyone from France and Germany to Greece and the Eastern European states will be able to afford it.
The EU might like to present itself as a single market, and it tries very hard to force people to set one price that applies throughout. However, the illusion is shattered when it comes into contact with the more diverse reality, and there's always a risk when you artificially distort markets for political reasons that you'll do more harm than good.