The righteous vindictiveness against people who run onto a field during a sports game is so bizarre. You want someone to jailed for this type of thing? This stuff is so common in Europe/other parts of the world, especially in soccer matches, and you rarely see stadium personnel or players physically assault the person who's entered the field in the process of escorting them away.
Being an immature, stupid buffoon doesn't mean you should be locked in jail. It does mean that you should be banned from attending future events, though, if you do this type of thing. It's disruptive and disrespectful to the teams/players.
As a final thought, I always find it amusing when players who tackle field invaders say "it's about our safety, we don't know what they have" ... so why did you run towards them and physically contact them? Why would you get closer to this person if you feared they might want to harm you? Doesn't totally make sense. IMO, let security/law enforcement do their job and apprehend these guys. Players physically intervening isn't a great look.