Spinning hypotheticals regarding alternative WWII event-sequences has long been a favorite activity of both myself, as well as many of my oldest friends. General Montgomery has long been regarded as insufferably vain, as well as limited in military acumen. Eisenhower's position as Supreme Commander is better understood in terms of him being the
in loco parentis, or the European proxy for the President of the United States. As such, many of Ike's decisions turned on political, rather than merely military factors.
Ever since Abraham Lincoln starting changing his top generals as often as he changed his socks during the US Civil War, every United States President expects a commensurate prerogative to micro-manage ongoing military operations. FDR was not about to let a mere 4,000 miles of Atlantic Ocean keep him from having a major say in how Germany was to be defeated. Eisenhower was NOT selected for either his strategic or tactical genius (geniuses being a dime a dozen); instead, Eisenhower was selected because he could be TRUSTED to enact the political will of Washington DC without letting his ego get in the way. Say what you will about Ike, when it came to being a personality, he was essentially EGO-LESS in comparison to Patton, Montgomery, and even Omar Bradley.
Lincoln did try to micro-manage the Northern side in the Civil War. However, he achieved what he wanted by firing incompetent generals, through arguably he waited too long in the case of McClellan. On the other hand, Bush 43 did not micro-manage enough, and it took the Republican electoral disaster of 2006 to get him to get rid of Rumsfeld and initiate the surge. Both he and Lyndon Johnson were poorly advised by appeasers, as was Truman with respect to Korea. In the case of Vietnam, Nixon only intensified the war in 1971 when the 1972 election campaign was approaching.
FDR and Lincoln's micro-managing was successful. Both were committed to victory and unconditional surrender of the enemy. No president since V-J Day has been so committed, and we have not won a war since then.