after that we put an imagined flight from very south of Europe to USA
Y'all might want to consider simulating more than one flight on a direct route before concluding it is the solution to all solutions...
. Like maybe try it with all the airplanes direct...
But, taking the discussion slightly more seriously than it perhaps deserves, is the problem really the number of ATCOs? Are direct routes limited by ATCO workload (and by inference number of ATCOs) or by airspace. Suppose all the flight paths were calculated by some big computer, across all centers in Europe (for example). Given the same separation minima (5/1000'), how much better would it be able to do? Or are there just so many flight levels available?