Given how prominent of a role the colloseum played in ancient rome, I was wondering whether there are any reflections on the institution handed down to us? Whether that be critical or praise or just reflections into the appeal of it.
Interesting question! We do have a fair bit of ancient thoughts about gladiatorial games.
Some authors, notably Seneca the Younger and most Church Fathers, found them distasteful, which you can read about in answers by u/XenophonTheAthenian (here), u/wedgeomatic and u/Tiako (here), and it is also mentioned by u/Amiedeslivres here. Being overly fond of gladiatorial games was also something associated with bad emperors (see Suetonius, Life of Claudius 34; Cassius Dio 73.17-21; Herodian 1.15).
At the same time hosting these games was seen as a sign of one's magnanimity, as u/lukebn has described here. This can also be seen in the poet Martial's work Liber Spectaculorum, which is more or less entirely about praising the emperor for his grand festivities, including gladiator fights