I think it was usually more of a warning. But I’ve read that this was apparently a thing in Shakespearean England.

Not just Shakespearian England, but also the post-Roman Germanic polities, Celtic societies, Early Modern Europe, Industrial Age Europe, etc.

Public executions used to be an occasion for picnicking even as late as the 'enlightened' 19th century AD, when norms regarding death began to get a bit more squeamish.

The notion of death alone as a reason for horror is very modern.

’Ordinary’ Roman citizens were still above average in the Roman caste hierarchy.

It wasn't just citizens who attended the games, man.

Yeah, like getting caught defending their countries from the Romans.

Noxii were more often bandits, rapists, murderers, etc. There simply wasn't enough of an influx of war prisoners most years to allow for them to be wasted as arena fodder. Even when war prisoners were used in the gladiator games, it was usually as damnati, who were not expected to die, not noxii, who were expected to die. Why would you waste warriors who had already indicated that they were willing to submit to Rome's mercy by simply killing them, after all?

Rebels were sometimes condemned as noxii, though.