Interesting that nobody has noted that the real problem is the design of the airport terminals that require all aircraft to cross active runways to the central terminal buildings.
From a throughput point of view it would be far better to have multi-mode runways so as an aircraft touches down a departure lines up and as the arrival clears the runway the departure takes off to be airborne before next inbound is at 2 miles. There are no wake turbulence delays as the departing aircraft wake is not interfering with the landing aircraft and vice versa. Imagine if you like 4 Gatwicks alongside each other. So the airport has widely spaced non-interfering approaches to widely spaced runways with terminal buildings between each pair of runways linked by underground rail to the other terminals. Each terminal has two potential multi-mode runways alongside that will not require runway crossing after landing or before takeoff.
But why think about airport design let's make do with the way it's always been done.