You don't need a 4th primary to
represent all visible colors. You just need imaginary primaries. Heck, even something with real primaries like Rec. 2020 [1] can represent information outside the standard sRGB primaries that a 4th primary would be useful to display. (Granted, a better choice of green primary would work better in that specific case, but such choices aren't always physically realizable.)
Another use is enhancing saturation of an image. My DLP projector has a mode like this to take advantage of its 6 primaries. Enhancing saturation can produce a convex gamut even from a non-convex one (e.g. sRGB), the only means of reproducing of which may be with additional primaries.
By my estimation, the main problem with Quattron wasn't that it had a 4th primary, which is legitimately useful. It's that - as you point out - it didn't. It literally did not have a yellow primary; just a yellow filter illuminated by the red and green primaries. Thats, like, total hokum.
