Circles would have had a couple of advantages. First, I believe they would have been easier to make. From what I've read rectangles have more stress at the corners. Rounding the corners reduces that but it is still more than circles have. With circles they could have more easily made bigger CRTs.
Second, there is no aspect ratio thus avoiding the whole problem of picking an aspect ratio.
Electronically the signals to the XY deflectors to scan a spiral out from the center (or in from the edge if you prefer) on a circle are as easy to make as the signals to to scan in horizontal lines on a rectangle.
As far as I can tell that would have been fine up until we got computers and wanted to use TV CRTs as computer displays. I can't imagine how to build a bitmapped interface for such a CRT that would not be a complete nightmare to deal with.