Invertibility is not trivial, and because full-field imaging is typically shift-variant this is a hard sell compared to Hartmann mask ( or lenselets) approaches which have none of the calibration steps.
I work in this field. I think they are motivated by novelty.
Actually, lenslets/Hartmann mask are not shift-invariant, and getting depth info (3D) requires loss of shift invariance (see http://web.mit.edu/2.717/www/stein.pdf). Lenslet-based light field cameras also have very extensive calibration routines to align the lenslets on a per-pixel basis.
You can either build a system where the field lands on the detector in a known way, or build one where it lands in an unknown way and try to figure out what the heck happened. In light of many functional designs (for example, Phasics, Zygo) I don't see why your group introduces the unknown factor. Could this have been done by a camera from Phasics?
I work in this field. I think they are motivated by novelty.