That's by design, of course. It's long been standard practice in the television industry to avoid showing any fans straying into the field of play to avoid encouraging that kind of behavior.
However, in the age of cell phone cameras and YouTube, a quick Internet search can reveal the on-field action in simple manner, showing the fan's exploits for all the world to see.
Considering the interest in fans on the field coming from fans at home, it bears asking the question. Are TV cameras shielding the eyes of the multitudes who actually wouldn't mind seeing some bozo clotheslined by a security guard, or even tased?
It doesn't take a genius to know that running onto the field is a bad idea, no matter how many times you live. The bottom line is, if someone does it, they'll be escorted off, probably in a rough manner, and then probably taken to spend the night in police custody. At the very least, you would expect that person to have a hard time going forward finding a ballpark willing to allow them in.
So, is there harm in letting them get a little airtime on TV?
Should TV networks show fans running onto the field during games?