Don't forget planes all file flight plans ahead of time so not only is there more space, but it is relatively easy to check for potential conflicts before flights leave the ground.
Flight plans are filed in advance, but a flight plan is just a plan. It's an impossible task to predict where an airplane will fly in advance, there are so many variables involved.
Just some of the many reasons a flight will vary from flight plan:
-Avoiding convective build up (thunderstorm)
-Avoiding turbulence for passenger comfort (changing altitude)
-Unexpectedly high headwinds (changing altitude)
-A cold front causes winds to shift, so the runways in use change
-Low clouds limits arrival/departure rate, so holding is needed
