The simplest political rationale here is that by the time of Overlord the bulk of forces committed to combat were under an American general. In North Africa and Italy the troops committed were equal and in North Africa, the high command at most levels was predominantly British as this did reflect the geopolitical realities of directing the war against the Germans at that point. Two British and one US army versus a large contingent of Axis troops that were mostly Italians and two German divisions.

In Italy, honors were even and command was more evenly distributed between the US V Army and the British VIII Army, with both US and UK forces sharing elements of the theater command.

In France, by contrast, there were three army groups and one British and one French army and everything else was US bar a small number of Polish troops and a few other odds and ends. The USA, politically, would see Viscount Alamein in Hell before giving him command of that many American troops, and the British were never willing to accept this at the time, let alone later. This is why so many of the command controversies of 1944-5 happened. As far as Bernard Montgomery was concerned the Germans were minor details and his real enemy was Dwight Eisenhower, who denied him the ability to freeze the entirety of the rest of the Allied force for a singular British thrust against a German army that would itself be magically frozen in place and ignore both the flank and the nicely long and vulnerable supply line and not at all use the aggressive methods that the Germans were known to use on a regular basis through the war.

Eisenhower was where he was because he was politically able to direct Montgomery, Bradley, and Devers to wage a war largely focused on the Germans, if having to more frequently remind Montgomery to look to the east, not to entertain the idea of commanding SHAEF. His ability to do so was sorely tested by the British, as late as the spring of 1945 insisting that he was incapable of directing the forces at his disposal and needed a British ground commander in his stead, in spite of a remarkably poor set of command performances on their own without the aid of one or the other major allies to aid them in combat.

As an example of that contrast, the same generals who presided over a disaster at Kasserine from a US perspective, minus Fredendall, were sent to Normandy where they battered through the bocage and proved to be far more able at mobile war than they ever were in Africa, in 1944. After two years of warfare.

After 1939, 1940, and 1941 against Germans, the British Army in North Africa was routed at Gazala in spite of having approximately the same amount of armor and artillery Montgomery would use to win his decisive victory at Second El Alamein. And in spite of having most of the same corps and division commanders, as well. The British of 1943-4 tried independent offensives, too, and the results were Market-Garden and the Dodecanese offensive, both of which are signal failures and confirmation that being able to clobber Mussolini's army did not prove the British able to face even small German offensives without Soviet and US aid.

So in that, too, there is its own justification for the role of Eisenhower and of the command he had relative to the British. So too is the reality that the views of Devers and Bradley toward the British was, shall we say, the kind that reciprocrated fully Montgomery's view that the American army was incapable of conducting warfare above a platoon level under its own officer corps. That kind of attitude in high command would have destroyed itself against Germans. There was no-one else who had the same aptitudes to high-level coalition command that Eisenhower did in the US officer corps, so he was fairly assigned to the position he held and he conducted it as well as it could have been done....which for all of his gifts was often not well at all and tied up in time wasted in the endless whining that there needed to be anyone but Eisenhower in charge while the Germans had their own squabbles but tended to be slightly better at setting them aside when the shooting started.