Almost every radio personality I've heard on this topic agrees that what the Saints (and probably many other teams) did was morally wrong. What is less clear is why it's wrong.
Most of the reasoning I've heard has been of this sort: bounties cause excessive harm, and causing excessive harm is wrong. The excessive harm could be physical--things like torn ACLs and concussions. It could be financial--the loss of revenue that occurs when star quarterbacks are knocked out for the year. Or it could even be moral--the damage done to the moral development of young athletes whose coaches use a bounty system.
I think this is the incorrect way to understand the wrongness here. It should be seen as a violation of a player's rights. Harm is often difficult to assess and sometimes a wrong can be done without causing excessive harm. But rights violations are clear-cut. Take the case of a simple boxing match. This is one of the few times it is perfectly OK to punch someone as hard as you can with the intention of knocking them unconscious. Why is it OK? Because your opponent has given you permission to try and do this. In contrast, I don't think any NFL player enters the game giving other athletes tacit permission to try to (intentionally) injure them. Injuries are collateral damage, or a double-effect of normal play. When a player enters the field of play, they freely assume these risks, but they do not say (tacitly), "You may try and tear my ACL," or "you may try and give me a concussion." Intention is key here. It is morally impermissible to intentionally touch another person in a way they have not (at least tacitly) given you permission to do. Thus, when a player intentionally tries to blow out an opponents knee or concuss them, they engage in impermissible behavior. This might even be legally impermissible, in addition to being morally impermissible.
In sum, the reason bounties are morally wrong is that they require players to violate the rights of other players--the right not to be touched in a manner to which they have not consented.