I'm familiar with the lens design limitations imposed by the flange-to-focal-plane distance. But what constraints are caused by the width of the lens mount (that is, the size of the hole in the camera body)? Clearly there's the fact that if your lens mount needs electrical contacts, they have to fit in somehow and you need to make arrangements for a diaphragm if the lens needs one. But what other limitations are imposed? For example, does it limit the maximum aperture of a lens?
A larger lens mount makes it easier to design compatible tilt/shift lenses.
The mount's throat diameter limits the exit pupil diameter. It also has strong control over vignetting, so it restricts the pursuit of ultra-large aperture lenses with acceptable light falloff.
With larger mount you can have larger exit pupil diameters. Ratio of entrance pupil and exit pupil is a measure for a lens symmetry. So with larger mount I suppose you can achieve more symmetric designs. The level of asymmetry affects among else depth of field (at given focal length, distance and aperture) and depth of focus. The look of out of focus highlights at very wide apertures is also impacted by size of the mount (and the chamber).