ETO & MTO would've been a grander position, but IMHO it would've been a bad idea.
Well the US position in the staff discussions of the time was that there should be a single unified commander for the ETO and MTO and CBO which the British reject on the grounds that its just a stupid Idea ( although they expresssed it more elegantly - As the source of Strategic direction is the CCS having another layer of command to give strategic direction is pointless and below him you need a level of command to deal with the war anyway. Also he system in use in the MTO works.
This is different from the Pacific theatres where the main issue is between the USA and USN. And remember that the USA at this point includes the Air Force.
What is SHAEF's role supposed to be?
He is supposed to be in charge of Logistics. ( dig and you will find the actual instruction to Eisenhower) but its not that simple. The Army Groups are responsible for their logistics from roughly corps on down and for most stuff ( and the bulky stuff is Artillery ammunition, Food, and POL but POL only if you are moving ( when you don't use so much ammo btw) they are drawing on national supply sources for ammo and food. And that's a defined distance back from the Front. The delivery route is factory - warehouse - Theatre - various depot with the AG responsibility being at a distance they can pick up and deliver to the front line units and cycle back and forth fast enough.
This gives a different situation for 21 and 12 AG. Montgomery who has done this before is operating from Normandy then from channel ports, which means almost as soon as it hits theatre its AG trains moving stuff and back from there its an overnight trip to the factories or stocks in the UK. 12 AG is inland and stuff from the US has a week or more transatlantic voyage with much more dependence on ADSEC and FECOMZ to move stuff forward from Cherbourg. And both of those are clearly under SHAEF. Where there is commonality is with POL which is universal. But the POL goes either to Cherbourg Normandy or Ambleteuse/Rouen from Mid September which is again much closer to 21 AG than 12AG.
And coordination of all of this is typewritten carbon copy memos , hand tabulation and sending the info by courier around the place or the occasional teletype which has to be encoded decoded. Noone gets a universal end of turn report unless someone sends it to them. So neither Bradley or Montgomery will be aware of the overall situation developing unless someone makes a point of telling them and telling them that its important.
And ofc Bradley and the US organisation has never really done this at the intensity of ETO operations. And SHAEF also has to deal with supplying France which neither AG have to bother about.
Market Garden and the Scheldt.
The Key decision point is 20 August which sets the general theme of the advance from Normandy which gives orders to 21 AG to '“The quickest way to win this war is for the great mass of the Allied armies to advance northwards, clear the coast as far as Antwerp, establish a powerful air force in Belgium, and advance into the Ruhr.”
So the plan at that point is for 12 AG to fight house to house through the Ruhr, so its surprising that Montgomery offers a sensible alternative like not fighting housing to house through the Ruhr. So the argument is not between take Antwerp and charge across Germany its between house to house fighting in the Ruhr and using firepower and mobility on the North German Plain.
Montgomery is right, Eisenhower horribly wrong and it takes Brest, Aachen and particularly the Hurtgen to show him that conclusively. Its an understandable decision but its actually wrong. Montgomery is also probably wrong on timing but remember this is actually the plan for 45.
The order coming out of that are to advance to Antwerp and take the docks, not to clear both sides of the Estuary. Why would they be. On that date noone knows the German position will collapse over the next fortnight and the Port facilities will captured intact. And this has been the Allied problem to date, destruction of the port facilities. So 11 Amd is given clear instructions to capture Antwerp and the Port which it does on 4 September. It is further ordered to then rest and refit as its just done a massive advance and has about half its armour in need of maintenance. They actually do try to cross the Albert Canal on 4th Sept on general principles but they have no positive orders to do so.
But the German position does collapse and both Dempsey and Patton enter pursuit mode. At this point there are two points of view. Either the German Army is permanently irrevocably routed ( and Bagration is happening so hmm maybe) or its not and at some point they will be able to stand. For Dempsey and Patton that does not matter their job is to keep advancing and get as much favourable ground as possible before the stand, because eventually the attack will resume in full force the only question being whats in front of it.
For Patton its the Moselle ( which he tries to bounce and fails about this time) then the Vosges then the Maginot Line, then the Westwall then the Rhone then the Harz with the next strategic objective being Munich. For Dempsey its the river lines, no mountains no fortification and if over the Rhine flat ground to Russia. 1st US army is not in Luxemburg until 9 September, and 9th army still around Brest until 19 September. And parts of both are immobile to keep Patton moving.
On 2 September, two days before Antwerp is taken. Dempsey/Montgomery propose Operation Comet which is a coup de main operation to seize the river crossings at Nijmegen Arnhem and Grave. This would use the British and British Trained Polish airborne who are trained for coup de main operations and its really there to prevent the germans blowing the bridges as the Armour advances. It does not happen mainly due to weather and when the order comes back Dempsey is dubious he has lost a week and is conscious that german 15 army is falling back into Holland in front of him, and they now have time to prep the Bridges so he starts arguing for a right turn through the Reichswald.
At which point Eisenhower has come back with an OK and London is pressuring Montgomery to take the V2 launch sites around the Hague. From Dempseys or Montgomery's point of view Market Garden working is great if it works and if it does not its better to attack now when the Germans have had a fortnight to prepare defences than in a month or 6 when they have had that much longer. Following the operative plan they will still have to cross that groudn the only question is when.
They have the fuel to do this. Horrocks says he had about 100 miles worth in his fuel tanks on 6th and more to hand so XXX corps at least could advance to about Arnhem. And half the additional tonnage eventually delivered for Market Garden was to support the US airborne divisions not originally needed ( so plus 250t per day to support XXX corps is the requirement.) MG starts on 17 September ends on 25 September with subsequent fighting being German counterattacks which fail.
Meanwhile in Antwerp. On 6 September the Germans start pulling 15 army out of the Pas de Calais this puts about 90,000 troops in front of 21 AG around Antwerp btw. The British are about 12 miles short of cutting off Walcheren Island with the Albert Canal in the way and German occupied on the South bank as well 13 September 4th CDN amd tries to take the Leopold Canal. and fails. This is the part south of the Scheldt which the Germans are retreating over. Simonds prioritises the Channel ports until Switchback on 21 September to clear the south bank of the river, 2nd of October the Canadians start attacking North of Antwerp against a numerically superior german force and succeed slowly sort of. They actually cut off Walcheren by 10 October.
9 October Eisenhower gives irrational and ill informed orders to prioritise the attack around - over holding the Arnhem pocket - on the basis that the Canadians will not be able to attack until 1 November because of lack of supplies, this is wrong its lack of infantry and the god awful terrain with canals and inundations everywhere requiring infantry. the battle actually ends on 3 November