J, if you didn't bring enough penis for everyone, you shouldn't have brought any penis at all.
Schools like to feel special and adcoms like to think that if they admit you, you will go. Both of those can really only be accomplished through the PS, unless you also submit an additional essay on that particular school (e.g. the Why Penn essay). I got into schools who (sorry for the bragging tone) probably should have rejected me since I was way above their numbers, which I attribute to including a paragraph at the end of my PS that was tailored for each school. I used the same general format, substituting the name of the school, the name of the journal I was interested in or clinic I wanted to do, and Professors whose work I admired. It doesn't take that long to do but it really makes a world of difference, IMO. ETA: you can still have the PS about your experiences, but I would recommend adding a few sentences about how that particular school will help you capitalize on those experiences, translate them into a career, etc. Help the adcom picture you at their school and taking their classes. Anything you can do to make yourself a person rather than an application can only boost your chances.