NZ767 said it perfectly. LHR can only hold so much.
Yes, there is a market for LGW alone. If Open Skies were to be reached, LHR would see the mass majority of long-haul international service. Infact, if there were room, all the US carriers would probably move to LHR and dump LGW.
So what would essentially happen to LGW is it would become a major domestic airport. What I mean by domestic, I mean it would have lots of service from Europe. Gatwick is very convenient for those who live in the countryside which is why it would still be popular for Europe service.
But when it comes to international service from North America, South America, or Asia, I think most of that traffic would move to LHR.
But like NZ767 said, there is only so much that LHR could hold.
Basically, LGW would become like Stansted, just a busier larger version of it. It would be "London's Domestic Airport" while LHR would be "London's International Airport".
Again, when I mean by Domestic, I'm talking about the entire continent of Europe, and not just the United Kingdom.
LGW would be popular by low-fare carriers like Ryan Air. So truly, if Open Skies would be reached, Gatwick would become a low-fare airport populated by a lot of low-fare carriers.
This is my prediction.
But it really doesn't matter, because it doesn't seem that Open Skies will ever be reached between the US and the UK.
"Generosity is giving more than you can, and pride is taking less than you need." - Khalil Gibran