Manhole covers are often round as it stops them being accidentaly dropped down the manhole. Period.
Many round covers have a notch in one side that fits over a protruding piece in the rim, so the reason given for easy replacement does not stand up.
Covers in Europe sometimes consist of two right-angled triangles attached by a loose bolt in the middle. These 2 pieces together form a square. This stops rattling as traffic passes over loose covers, as teh triangle will sit firmly on a slightly uneven rim, unlike a square or circle, which will rock in the same situation.
For anyone who has tried, a full-strength cover, intended for use in heavy traffic situations, is quite heavy and it is easy to drop down the manhole. Nothing to do with being a Sanitation moron, rather to do with being a lightly-muscled engineer!