A heavy motorcycle is harder to use in slow speed, stop and go, mount and dismount scenario. A guy dropped his BMW (I think) bike in front of my house some time ago, and it was hard for us both to raise it. An LEO in a densely populated city doesn't need a boat anchor, he needs a vehicle that he can drop and lift all by himself. It also helps if the vehicle is not too loud.
With regard to "looking like an idiot," I believe this concern is not even on the radar of most LEOs. Staying safe is the priority #0; a vehicle that won't crush you if a protester pushes you is a good start.
They call um horses. They can get back up on their own and step around worthless POS’s in the street. They also know when to void their bowel if you know what I mean.