Yes Americans still have to return home and still need seats on Europe-US flights. However since it is easy to separate the Europeans from the Americans based on where they originate the travel, Americans are still charged higher prices. THis is because during summer many AMericans visit Europe and the demand from them is high and they are willing to pay more.

You ask why don't they just sell all the seats to AMericans. The answer is because there are not enough Americans. Same reason they don't sell the entire cabin to full fare travellers. They would love to, but there are not enough people willing to pay. So instead they invent things like advance purchase and saturday night stay. These devices are used to separate those who are willing to pay big bucks and those who are not.

The key here is to create different classes so that you can get people to pay as much as they are willing to pay.

Imagine there is a plane with 5 seats and 5 people wanting to fly that route.

Guy A willing to pay $5
B is paying $4
C is paying $3
D is paying $2
E is paying $1.

You could sell seats for $3 and then three people would travel and revenue would be $9. Or you could sell seats for $2 and then 4 would travel and revenue is $8. But idea would be to come up with a way to make them pay as much as they are willing to pay. So guy A is willing to pay $5 and you make him pay that because he has no advance purchase. Similarily B is travelling to Europe for his summer vacation and is willing to pay $4. D is travelling from Europe doesn't care much about going to USA so he only has to pay $2.

Basically it breaks down to something like this: IF Americans are charged $1000 they will pay it and comprise 50% of transatlantic travel. If Europeans are charged $500 they will also be willing to pay that much and fill the other 50% of seats. The airline averages $750.

If the airline instead charged $800 for everyone. More Americans would now be willing to fly. Perhaps 20% sat home when fares were $1000 but now choose to go to Europe. So they fill 70% of the plane. But now Europeans are paying $300 more. Before they were filling 50% of the plane. But now that price has risen by 60% they only fill 20% of the seats. So now you have 90% of seats filled at $800 and 10% of seats empty. That means average revenue is $720 per seat. You lost $30 per seat.

What we are talking about here is differential pricing. What you are attempting to do is charge more for those who are willing to pay more but also keep those who are willing to pay less as customers. It commonly occurs with airfares because it is easy to separate people's willingness to pay based on characteristics like advance purchase, saturday night stay, and country of origination. However it happens elsewhere too. Women have long complained that they pay more for clothes, shoes, and dry cleaning. Probably because they are willing to pay more and therefore they are charged more. Electronics are often sold at a premium price when first introduced because those who are willing to pay more will do it when it first comes out. Then later reduce the price and those who are willing to pay less will then buy it.

I've tried to make this as simple as I can. It is a fact that Americans pay more for summer transatlantic travel. It is because we are willing to pay more and the airlines can not fill all the seats with only Americans so Europeans are given a fare break. It is not just the individual date.