"Was the flaw in the Sherman being so high due to the awkward transmission and drive shaft arrangement (clumsy American idea of running the driveshaft under the fighting compartment to reach the drive sprockets at the front), or was it because they originally used those large-diameter radial engines, and after switching to other engine layouts it was deemed cost-ineffective to redesign the hull lower, as that would've slowed production initially to accomodate the new design?"

According to one of the British battlefield documentaries, the problem was that the Americans had neglected the development of tank engines, pre war, and were forced to use a modified aircraft engine which gave the Sherman a higher silhouette.

The Sherman was a very good tank when it was first used in combat at the battle of El Alamein.  It also need to be relatively light to be transported from American factories to Europe. Once in Europe it had to be light enough to cross normal bridges when advancing. It was also enormously adaptable and reliable.

It did have a nasty habit of catching on fire. It was also, of course, too tall.