Exactly. Pixels are indivisible quanta, not units of any kind of distance. Saying pixel^2 makes as much sense as counting the number of atoms on the surface of a metal and calling it atoms^2.
This idea itself breaks down when we get to triangular subpixel rendering, which spans pixels and divides subpixels. But it's also a minor form of optical illusion, so making sense of it is inherently fraught.
Maybe a pixel is just a pixel.