Because it's not just running on the field that's the problem. If that were all, it would be a simple matter of imposing major penalties on those few. The temptation is to do a Rodney King right there in the middle of the field on the first guy who tries to slide into second base. Do it to the first guy, and you don't have to worry about anyone else trying it. Of course, that would be wrong, that's for sure.
Violence begets violence.
Instead, I'd see to it that anyone caught running on the field spent the next dozen weekends of his pathetic life washing graffiti off public buildings in the same Bronx in which the offense was committed. Like the cretins who threw the snowballs in Giants Stadium last year, every one of these people should be identified and pictured on the front pages of local newspapers. With any luck, they'll lose their jobs. But it's not just running on the field. There's a mentality of violence and thuggery that infects the entire building.