crisf

Each orbit is a spinning top. You pull on a top from the side, it's spin axis precesses.

Some do cancel out. The inclination effect isn't driven by the sun's being above or below the equator - it's basic rotational mechanics. The net effect of the moon and sun's gravity pulling on the satellite causes the rotational axis to precess. The precession shows up in the orbit as the change in inclination (and ascending node).

Regarding the non-random spread.... all the orbits start at the same place (0 deg inclination - because that's where people want them). And it's the same sun and moon affecting all of them them in the same way, so you wouldn't expect it to be random. It is interesting that they all appear in that band, I don't have a good explanation for that : )

The preferred geosynch orbit has an inclination of 0deg, as that minimizes it's apparent motion in the sky. But this requires a lot of fuel for N/S stationkeeping. The reason the orbits get inclined is because they're being pulled from the side by the sun and moon, and just like any other rotating object pulled by a lateral force, their axis precesses (just like a top). Left to itself, the orbit cycles between 0 and 14 deg inclination.