Metro man, I suggest you follow one of the flight tracking programs on the internet and see how few long haul flights follow great circle routes. On the north Atlantic the tracks are designated east and westbound each day. They rarely correspond to great circles between any points in Europe and the USA. The same goes for the south Atlantic to Brazil and Argentina. The likelihood of US ATC offering great circle routings, even under Free Flight, is unusual.
On the Pacific between Australia and New Zealand the routes change, sometimes minimally, on a daily basis.
The components you list which determine routes chosen are all valid but in over fifty years of listening to HF broadcasts, in over thirty years of flying long haul as a passenger and closely following routes taken, and years of organising professional conferences for ATC management worldwide at which route planning was regularly discussed, I have only rarely come across flights operating a true great circle route.
Minimum time tracks are used to minimise flight time for passengers, for airframe and engines and, using advantageous winds, to save fuel and have become the industry standard.