Old airports have terrible runway design, the runways intersect (to save space) but this is dangerous and requires much more ATC coordination to manage. With modern runway design, if a plane takes off or lands out of sequence, it's unlikely to hit anything. With intersecting runways, that same accident becomes potentially fatal. These airports were also designed for smaller planes, fewer planes, and less passengers.

These issues are obvious to airport management, but airports cannot expand because nearby land is already allocated. The easiest option is to build a new airport, far from existing development.

Most of these airports were originally built far away from the city, but in the past half century the cities expanded so they new envelop the airport.

Less room for error, can't build extra runway(s) to cope with increasing demand. The current Mentour Pilot video actually discusses this issue in some depth re one of Washington DC's airports.