Should a certain type of player be reported and possibly punished?

The type is those that laugh at and pick on a team that was trolled by toxic player(s) who intentionally feed and then quit, leaving their team completely screwed over, and giving the other team the advantage...

set aside the trolling, they are definitely reported and punished (or at least should be). Those on the other team, however, IMHO need to be warned for their behavior. Laughing at a team who was put at an intentional disadvantage because of someones toxic behavior, is unsportsmanlike and shows support for that toxicity, just because it gave them an advantage. I have seen tons of good players (including myself) who learn the other team got intentionally trolled by someone trying to ruin their game, and then express sympathy and support for those affected. That is how you follow the code. Making fun of those who suffer, is the lowest of the low, and shows the same character as those who make immature jokes and comments after a disaster (remember the trolls that surfaced after the Japan Tsunami). These people should be held accountable for their actions.

As I've said hundreds of times:
"The way to stay out of the tribunal is to follow the Golden Rule, and treat others, as you would like others to treat you"