Nope Hitler could not decide were the attack would land so he created Panzer Group West which on paper reported to OB West but had to be activated by Hitler himself. This convoluted setup came about because of the famous dispute between Rommel and Everyone else about the deployment of Armour. When the invaision came the commander of the 21 Pz (Feuchtinger) did not no whether he was commanded by 84th Korps, 47 PZ Korps, Pz Group West so he waited for orders from Army Group B. Geyr the commander of Panzer group west could not activate his command until Rundstedt got permission from OKW. When Jodl at OKW finally gave permission at 4pm to release forces
12SS and Lehr were placed under the command of 7th Army which was part of army Group B. 12 SS attack on the 7th was delayed because the nessecary petrol was not available. When Pz group HQ west arrived (incidently not 230 miles away

) It took charge all under army Group B (Rommel) 7th fought the Americans and PZ West took over the British sector as units were released they joined one or the other. Pz Grp West changed name to 5th Pz. So basically when a High command interferes in operation there is chaos thats why they leave it to the HQs. These Reserve formations might be sitting on depots of supply but they are in reserve for a purpose so as they dont expend resources like Front, units niether are they at 100% readiness they also cant take those supplies with them because their deports are usually at place easy to supply like railheads. Next you have the chain of command to actually get them to move. Then you need supply dumps in place at their destination. Nope High command units should have no flexibilty at all sure they should have a lower CC and use less supply but no way should they be performing like they do in game.