I don't have an answer, I'm just wondering out loud.

Cone cell activation is complicated. Displays with three well chosen primaries are economical and effective, but they aren't intended to produce every perceivable color. And our chromaticity diagrams, that pointy splotch that's often used to compare display gamuts, is based on a "standard observer" that is a simplified model for human perception.

An ideal pixel would be able to emit any kind of electromagnetic radiation of any intensity, kind of fun to think about but unrealistic and impractical.

What additional primaries mathematically do is expand a gamut from a triangle to a convex polygon. While ten or a hundred primaries would be bonkers, I bet we could fit a quadrilateral or a pentagon to the perceivable gamut in ways that'd see some gains.