No. The largest possible square supported by the 43.27mm image circle common across the EF lens system is just under 30.6mm x 30.6mm. Anything bigger than that would result in corner shading.
The goal is not to get a perfect square output, but to get the maximum the image circle can produce. It's better to crop corner shading in post, than to crop a large fraction of the image circle with every shot.
- Some EF lenses have a rectangular baffle, such as the 70-200, optimised for a 3:2 image format. This would allow for a theoretical maximum 24x24mm square sensor
Remove the baffle and stop producing lenses with such baffles. Do they serve any specific purpose which can't be accomplished with other features?
- Many lenses have petal shaped hoods, optimised for a 3:2 image format. This again means a 24x24mm sensor Replace the hood. Plastic is cheap.
- If using the DSLR format, the 44mm flange distance would be pushed over the limit to allow for a 36mm image height mirror - This was addressed in a previous post: this large sensor would either require a major redesign of the mirror assembly, or would need to wait for maturity of mirrorless.
