Back on topic, I think baseball games are the LEAST offensive venue for strollers, especially if you are in the GA area. There are lawn chairs that take up more space than a stroller, and I'm a fan of allowing lawn chairs in the GA area.
I get the "child on the shoulders" argument, though I don't agree with it. Unfortunately, we live in a litigious society. If some careless parent (or wild-arse child) caused the child to fall off of his/her parent's shoulders, the parent might find it prudent to sue the university for owning property that caused the child to hurt himself/herself for falling on it.
@Froglaw, that's one of the many reasons I no longer park in Lot 4. Another is that I did not have the room that you are afforded by having a spot next to grass in which you can "sprawl out". I couldn't have anything extend beyond the Fire Lane, so my canopy basically shaded my pickup and we grilled and sat in the blazing Aug-Oct sun. My new spot is awesome, and less than half of what I paid for that spot. It's about the same walk and I don't get points for parking anymore, but I'm good with that. I'll try to edit later with pics.