Shooting Patriots at flying lawn mowers (I suppose you mean Shaheds, Gerberas, and the like) is crazy. Patriots are key to shooting down ballistic missiles.

To the best of my knowledge, the explosives-laden lawn mowers flying over Ukraine are mostly destroyed by cannon fire from the ground, cannon / machine-gun fire from aircraft (including converted GA aircraft), and interceptor drones.

I expect the US armed forces to be testing oodles of various cheap drones by now. E.g. the US has used Shahed-lookalike drones while attacking Iran recently.

I believe THAAD is for ballistic

Patroits for cruise missiles and jets

Other for one way suicide drones

I'm unsure if Ukraine has used patroits against ballistics. My understanding is that is a low count in the Russian mix. Cruise missiles and jets are their primary targets in Ukraine (aiui)