> Why would it be uncomfortable? Those hidden inside the (original) machine were not exploited by the machine owner
Do you have a source for that assertion? As far as I can tell, several of the chess players known to have operated the Turk had substance abuse (chiefly alcoholism), health, and money problems (the words 'debt', 'penniless', and 'destitute' come up a few times). While not proof of abuse, it does suggest a strategy of recruiting the vulnerable.
In late 1700 and early 1800 Europe being a heavy drinker, having some kind of health issue and/or being penniless were the norm for most of the population. If performing a task because of those issues means being exploited then we must assume that almost everyone in Europe at those times were exploited in one way or another.
I understand what you mean if we judge it from modern western standards, but I don’t agree if we judge it by the standards of that era.
edit: I see that wearywanderer explained what I mean as a sibling, that’s why I think GP didn’t get precisely what the MT was and how it was operated