I’d say the modern American movie and TV audience is about as bloodthirsty, but through the miracle of special effects the victims aren’t actually dying.
Whereas we have the spectre of blood in the streets, the Romans had the real thing. :’)
They started slow, with a ritual struggle that was at least occasionally part of funeral rites, and of Etruscan origin. The Roman way was to have a duel between two gladiators of some sort, slaves or criminals who had no real choice than to participate. Eventually larger, longer festivities were mounted as memorial to very grand people, and they were opened to the public. I’m sure there were carpers carping about how this wasn’t how it was supposed to be done. The competition between the great families of the republican period led to larger venues. The arena in Pompeii (which was over a century old by 79AD) seated more people than probably lived in the town.
Here’s a link to a tomb painting of a hooded man on a leash of sorts, trying to fight off a vicious dog. I think I’ve seen a similar tomb painting with two dogs. It’s very possible that this portrays a special penalty, perhaps the punishment of the murderer of the deceased. Etruscan inscriptions are short, practically no long texts exist, and it hasn’t been cracked to the satisfaction of the consensus-seekers.