The pins/struts are a 2 point system that double as the booster lift points in general operations. The booster mostly hangs in tension which the existing tank structure can support. I would guess they share some of the structure beefiness with the grid fins.
Legs require at least 4 points, probably more. Shock absorption hardware, ability to unfurl to an acceptable width. Require reinforcement (cross bracing) near the base of the tanks to handle the loads pushing inwards toward the center of the tanks.
You can technically imagine two legs with really wide feet, allowing some perpendicular stability. I wonder if one-leg lander could be imagined. 3-legged landing scheme was used in Surveyors, first American automatic Moon landers, and was surely considered for Appolo LEMs, but rejected. So there could be additional, secondary reasons when choosing the number of legs.
4 legs have no additional redundancy over 3. One leg failing will still result in the booster tipping over. They do push the maximum angle of tipping before your CG is no longer supported out farther though.
Legs require at least 4 points, probably more. Shock absorption hardware, ability to unfurl to an acceptable width. Require reinforcement (cross bracing) near the base of the tanks to handle the loads pushing inwards toward the center of the tanks.