The probability of mid-air collisions actually went up in step with the finer granularity of GPS systems.
> The navigation paradox states that increased navigational precision may result in increased collision risk. In the case of ships and aircraft, the advent of Global Positioning System (GPS) navigation has enabled craft to follow navigational paths with such greater precision (often of the order of plus or minus 2 meters), that, without better distribution of routes, coordination between neighboring craft and collision avoidance procedures, the likelihood of two craft occupying the same space on the shortest distance line between two navigational points has increased. [1]
It got to the point on many routes where regulators had to mandate an offset in opposite directions along common flight paths to effect "lanes" of traffic. [2]
[1] https://en.wikipedia.org/wiki/Navigation_paradox
[2] https://en.wikipedia.org/wiki/Strategic_lateral_offset_proce...