airplanes fly at different altitudes in different airspaces (places around the country) and in all 4 different directions.

heres a simplified example.
going east there are appxly 10 different flight levels. lets say every other odd number from 21, 000 ft on up. 21, 25, 29, 33, 37, etc thousands of feet asl(above sea level).
going west there are appxly 10 different flight levels.
lets say every other odd number from 20,000 ft on up.
24, 28, 32, 36, etc thousands of feet asl.
going north there are appxly 10 different flight levels.
lets say every other odd number from 23,000 ft on up.
27,31, 35, 39, etc thousands of feet asl.

lastly , going south there are appxly 10 different flight levels.
lets say every other even number from 22,000 ft on up.
22, 26, 30, 34, 38, 3tc thousands of feet asl.

if you study this...you will see that minimum seperation is at least 1000 ft in any direction.
going in opposite directions ,flights are usually routed into air corridors to keep minimum seperation of at least several miles horizontal and at least 1000 ft vertical.

so, even with 5,000 plus commercial flights in the air at any one time over the whole usa...thats a pretty slim chance of intrusion into another aircrafts safety zone.

plus with the air controllers, pilots and computer avoidance equipment... the situation is sager than on the local freeways.
over the whole usa

blessings,
dr james
retired cfo, pilot and air surgeon