Each pixel of such a scanner would need to somehow scan the spectral content. For example, imagine an array of fibers each transporting light from image plane pixel coupled to a spectrometer (bulky, expensive). Slit (a.k.a. push broom) scanners take each pixel of its slit and disperses the light perpendicular to the slit onto a 2D sensor array (more compact, 1D mechanical scan required). I recall seeing spectral (color) filters made from dispersive materials sandwiched between rotating polarizers to filter (scan) the light entering camera (expensive, compact).

A linear scanning mechanism would be a lot faster still than the XY approach.

I'm very curious how expensive sensors are though, that capture this data in a single shot, I've not seen any prices so far.