There are many differents kinds of military generalship. While Grant may not have been a "great field commander," he was rare among the military talents of the day in several ways: 1) he won battlefield victories, something most of his Federal colleagues couldn't or wouldn't do; 2) he had a good strategic sense, in his plan to invade the south by using the Tennessee River as a "logistical highway;" 3) he had a knack for picking good corps and division commanders and promting men of talent (e.g., Sherman, Sheridan) and getting rid of those without it (e.g., McClernand); 4) like Lord Montgomery of Alamein, Grant was not imaginative or dramatically innovative on the battlefield -- he was simply bulldog tenacious. After accidentally colliding with Lee's army in The Wilderness, in forty days he drove the Confederates into box perimeter around Richmond from which they could not break out. When they finally did in April 1865, the war was quickly forced to conclusion; 5) most importantly, Grant had the confidence of his Commander-in-Chief, President Lincoln and in our system, the military is always subordinate to civilian authority. All other Federal commanders were found wanting in some key respect -- Grant carried out the policy directives of his superiors and did it without incessant demands for more men and material (which he got, in any event).
Grant's reputation as a butcher is undeserved. No Civil War general was able to solve the tactical problem presented by the rifled musket, which made traditional Napoleonic battlefield tactics obsolete. Indeed, this problem was not really solved finally until after the bloodbaths of The Great War, with the advent of the tank, which returned mobility to battlefield action. Until then, defense, trench warfare, and high body counts dominated the tactical playing field. One cannot denigrate Grant as a butcher without also doing the same to Lee, whose aggressive and inexhaustable use of irreplacable southern manpower was often commented upon by many Confederate civilians. Only after the war, as part of the rise of the Myth of the Lost Cause, was Lee elevated to secular military sainthood.
Grant was a good general because he accomplished his military aims. You can criticize a much of his performance, but he understood the stakes and dimensions of the War and was unwilling to adopt a tentative, hesitant tactical approach. His doctrine of "pursue the enemy army, wherever he goes" was the key to finally defeating the Army of Northern Virginia.
Generally concur with your post but Montgomery was/is the most overrated general of all times.
His "Victory" at El Alamein came against a foe whom he outnumbered 2-1 in manpower 4-1 in tanks, 3-1 in planes, and 10-1 in artillery -- and the Axis forces ran out of gas!
In Normandy, the inability of his forces to achieve their D-day objectives brought on a bloody battle of attrition where he was losing three men to each German casualty. His Operation Goodwood resulted in the loss of 470 tanks in four days for little gain after tremendous aerial bombardment.
The one thing Montgomery was master of was spin control. He pretended that all of what was happening was his plan (as if getting the British in a WWI type battle of attrition was a good plan); unfortunately for Montgomery's memory the paper trail is not there to back up his ex post facto claims.
See "Churchill and the Montgomery Myth" by R.W. Thompson where Thompson suggests that Montgomery's ideas didn't advance one whit from 1918 until the day he died.
Not meaning to bust your chops; Montgomery and his apologists are a sore point with me.
Walt