That's overly reductionistic. We're not paying to watch them strike eachother in the head with baseball bats. We're paying them for an intense display of athletic skill, which incidentally is also extremely risky and likely to cause long-term harm. The reality is bad enough without overstating your case or taking a naive view of what people are getting out of spectating.
By the time you were fighting in the amphitheatrum novum, you had already survived a bunch of other fights and proven your abilities. And of course the citizen of Rome came for the same "intense display of athletic skill". There isn't much enjoyment in just mindless slaughter, so you add animals and weapons and shields.
Again: the stupid, sensationalist comparison to bloodsport is not helping your case against anyone who doesn't already agree with you. Normal, rational people will read your comment and say, well, there are no swords or lions in football, nor any caesar giving the thumbs up or down, and almost no one dies on the field. Clearly this guy is off his rocker.