Why a different mount? The F mount is pretty small ...
Depth, not diameter, is the main issue. This is the same reason that no 35mm format rangefinder has a mount anywhere near the roughly 46mm depth of F mount: to reduce body size and allow great flexibility in lens design by allowing the option of far lower back-focus distance, meaning rear lens elements far closer to the sensor. (Yes, this can be done with "near telecentric lens designs": back-focus distance and exit pupil height are quite different.) [Added: like the Nikon rangefinders, whose lenses would need a lens mount shallower the "F" to be usable.]
... the NEX lenses are pretty large.
On one hand, Sony has for some reasons done the worst job on lens downsizing amongst current mirrorless systems: look at micro Four Thirds for far better exploitation of the downsizing possibilities, and it is not only the 25% difference in format size. In particular, the collapsable and pancake lenses give a body depth than neither F mount nor Pentax's K mount (as in the K-01) can match: the front of some of those lenses sits closer to the sensor than the F or K bayonet does.
On the other hand, it could be that for many lenses, the front elements end up about the same distance from the focal plane anyway, so that a shallower lens mount then just means that the lens body is longer. So maybe the strategy of the Pentax K-01 can be made to work: for the lenses that do benefit from a low back-focus distance, have the rear elements protrude back into the empty space where the mirror used to be. If this can be done well enough, then having the same overall camera+lens depth might give some advantage to the "deeper body, shorter lens" approach, because you have more room in the body for stuff like external controls and battery space.
Added: If the system is designed to support existing lenses via an adaptor, the main argument against a new shallower lens mount comes to "I do not want to have to use an adaptor". This seems a rather weak reason to hamper future lens design options, since one could simply leave the adaptor permanently in place. Maybe I am just insufficiently concerned about backward compatibility, like my skepticism of the idea that the ideal format for interchangeable lens digital cameras is 36x24mm.