IIRC, box pressed cigars are slightly underfilled when rolled so when they're pressed, the fillers compact to the desired density. I have a feeling that if you take a round cigar and try to home box press it, and although the end result might look alright if you're successful and don't crack the wrapper or something, the draw will most likely be too tight.

The first cigars that got a pressed shape were indeed tightly packed into the box as to slightly flatten the sides a bit, but deliberately box pressing, or trunk pressing, is a different process with the pressing in mind when constructing the cigar.