We are not talking about slavery of the last two-three centuries. These are completely different matters. Mereen is shown similar to Ancient Egypt, while the rest of the world - High Middle Ages, no later. In this part of Essos slavery is as essential as it was in Ancient Rome, or other civilizations of the Ancient World. Their entire economy is based on slavery, and slaves are used in a big part for hard, but essential basic labor. I am not saying she should keep them enslaved, by the way, I am saying that she shouldn't jump at and massacre free people because it is free people who provide skilled labor.
If a ruler wants to please everyone, it will be a disaster. Good ruling is not about giving people whatever a hell they want but about creating a stable social and economic organization, and it would require placing some limits on everyone. OK, Dany gave that guy three times more money for what his herd worth. Did she buy his loyalty? Let's say your neighbor has a pack of very evil dogs who are running around attacking things, and they killed off all your kittens and puppies. Your neighbor was in a generous mood and paid you three times their worth. Would you become his loyal servant? Why would you? Because you got a good compensation? What about his dogs who next time may kill your children? The wise thing is to take money and to get a hell out of there.
The same would be with that peasant. Dragons are still flying around, Dany has no idea how to control them, and the peasants, if they have any frigging sense, would just leave with the money. There will be less money in the treasury, and less peasants who can provide goat milk, hides, and meat, for the city. Sorry, but her paying up people is the dumbest thing economically. Give them new goats, make them work, trade, and pay taxes, not finance their departure.
I hope at some point she will realize that she is not suitable for leading any economic reform, and neither any of her advisers, and will find somebody as an equivalent of the hand of the king, who will deal with economic issues.