Nah, there is an upside. It's a free country as long as you mind other people's space. You wanna turn tricks? Have a con artistry business? Nobody cares. Free country, free enterprise, and no taxes. Just don't bully ppl. There's plenty good about the country, but only if you can understand how to live without hurting others.
Of course, it's easier for people with a business mindset than people who are only good at stealing.
Nudity wouldn't cut it as a deal. They'd need more than that.
actually you can bully people, but not physically. if you would remember how she got into this mess, she promised to do anything if she got aid. basically trading a future amount of labor of potentially massive amounts for some basic healing. stabilizing her father temporarily would allow them to name their price, and if she reneged of the deal they could end their stabilization, resulting in her father's death.
likewise let's say a criminal flees one of the northern city states with a ton of gold. then buys up a food market in a small village. now as we all now food doesn't grow year round, thus he has all the food for a certain distance (minus those that stockpiled their own supply). he could ask from the poor that didn't have enough to stockpile food for some additional labor or something else that seems reasonable, but in effect increases the cost. he can then leverage such gains to buy a wider radius of food control. then those in that initial village now can be charged even more due to the hardships of traveling further to get food, in addition to the fact that more people would have run through their stockpile. some would have left, but not all for various reasons. those that didn't or couldn't leave are now his personal slaves, living and dying at his whim. by leveraging this labor force he can increase his influence area, trapping more people and getting more slaves. as long as no one is allowed to rise up against him he can continue, unless someone else with money decides to counter him, at which point they would either replace him a the slave owner or be a benevolent leader. in any case freedom from bullying is the last thing you have.
granted if it was a true anarchy then he would have to worry about physical security against rebellion and such resulting in more operational expenses due to unethical treatment of his lessers.
as for nudity being insufficient, it is a matter of how much the sex slaving costs vs. how common nudity is. imagine that he pay $1000 a night, that people would only be willing to pay $1 for nude female fighters over clothed female fighters, and the stadium holds on average 300 people:
sex slave deal for 18 more nights equals $18000.
it would take 60 days of nude fighting to match the sex slaving.
it would take 3 months at S-rank to get all paid off, which is 50% more money.
if they stay as A-rank it'll take 6 months, which is double the money.
given what we know of this society it is easier than reality to pay for sex, especially for the rich, which means $1000 is high. we also know that there is a draw for sexual themed fights given the costumes and history of rape fights, greater than reality, so $1 is a tad low for extra drawing power. therefore this is a very conservative guesstimate.