But isn't the problem that a lot of airports (like Heathrow and Schipol) are operating at capacity? So the only way to get more capacity is to increase the size of each individual aircraft.
Sure, but they are designed for big heavy jets and the reason they are at capacity is because building long runways with noisy approaches is very controversial in densely populated areas.
There are many smaller airports in and around London that you can go to with a smaller plane and quite a few that are more convenient to get to from inside the city. If noise and pollution stop being concerns, many of those would be able to absorb the traffic and building more would be a lot less controversial.