Didn't the episode itself also address the issue of there needing to be a punishment for rebels? Kazuya was also extremely angry that he needs to get rid of a man as capable and far-seeing as Duke Carmine. If someone starts a rebellion against the king, it's not enough to just slap a collar on the person and then pretend everything's cool again. That would be an exceedingly acceptable risk for anyone planning a coup or just some more minor, but still big, crime (treason or not) in the kingdom. That's why I wondered what's the point.

Of course if there's no tradition of execution for a treason (or lèse-majesté) but instead the collar is used and the culprits are truly rendered into lowly slaves for life, it's a different thing. It could be pretty bad even if they weren't sent to the mines (which typically was a death sentence, just a slow one). Carla Vargas, for example, is a beautiful girl, so her fate as a slave wouldn't necessarily be a pretty one.