Are martial arts sinful?

This question has been bugging me for a while. I've tried doing my research, but I have seen good arguments from both sides and I can't come to a conclusion. I know practicing them as a hobby or for self defense is fine, but what about participating in and watching competitions (such as the UFC)?

On the one hand, those who say it is wrong say that the ultimate goal in such fights is to cause as much damage to the opponent as possible, which is wrong. The catechism of St. Pius X forbids inflicting harm on others:

1 Q. What does the Fifth Commandment: Thou shalt not kill, forbid?
A. The Fifth Commandment, Thou shalt not kill, forbids us to kill, strike, wound or do any other bodily harm to our neighbour.

I've also seen other people say that it would fall under the Church's ban on duels and tournaments (I'd say that's kind of a stretch, though). And there are many quotes from saints against gladiatorial games and such, as these glorified violence and excited sinful passions.

On the other hand, I've seen others claim that violence isn't always sinful, which (according to them) isn't the case in such competitions, as they are done for sport. Also, safety is a big concern in those fights, so the chances of seriously harming others are almost null.

On top of that, I've read that boxing was a big part of Catholic culture in the last century, and even clergymen participated in it. It would seem kinda irresponsible for the Church not to do anything againt such a widespread problem, if it were a sin.

Lastly, there's a passage in the Summa Theologiae that could be used to justify fighting competitions (but I personally think it would be more applicable to sparring sessions than competitions):

Summa Theologiae, Secunda secundae partis, q. 40 a. 1, reply to objection 4:
Manly exercises in warlike feats of arms are not all forbidden, but those which are inordinate and perilous, and end in slaying or plundering.