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Is there any context where it makes sense to have fractional pixels? Like millipixels, micropixels, nanopixels, etc.? There is of course sub-pixel text rendering; does anyone refer to numerical fractional pixels in that field (333.33 mpx)?

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I think the notion of fractional pixels is rare indeed. But I can think of one example from astrophotography. After taking a photo, we use software to analyze the size of stars - for features like autofocus, auto-guiding, and detecting smeared images. Describing the full width at half maximum (FWHM) of stars with decimal pixels is normal practice. It's akin to fitting a Gaussian function to a measured peak, and letting the Gaussian have a fractional standard deviation that isn't constrained by the integer pixel grid.

I guess on that note, video compression motion estimation/compensation can also make use of fractional pixels.

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