Im not talking about what basically amounts to rape, as that would be explicitly against itch TOS. What I'm talking about is some other way to gain the loyalty of the invaders you capture, such as having a dungeon to put them in or something similar to break their spirit and force them to work for you out of fear of punishment. I just find it odd that "oh, someone invaded me and attacked my servants, let me buy them gifts to make them like me!" is basically the only way to be able to get invaders to start working instead of just being bound in the cells or throne room. Adding in a system that is more in line with realistic approaches to irl 'indentured servitude' wouldn't go amiss. Could even make it so that the invader would do whatever job you assigned them, but they would still be unable to have sex with until they become loyal enough later on.
Well, you don't necessarily have to get them to like you to work for you at the moment. You can ask if they will serve you and they usually have a "buy-out price" based on how much they like you. It's basically the same as buying a slave. They work for you no questions but still hate you. Slaves are way cheaper, so unless you REALLY like someone you captured, sell them. I do think a fear/spirit-type system should go in place. Currently, the "Warden" trait only gives about 1-2 relationship a day if you have someone with the trait assigned to a jail cell (not a binding cell sadly) with a prisoner in it. So I think a "Torturer" trait would be a good alternative to that after a "dungeon" or "torture cell" is added. To note, anyone assigned to a jail cell will feed and clean the prisoners. A setting to tell the torturer whether you want them to clean and feed certain prisoners should be added, I ain't about to assume DM wants their slaves treated nicely (or certain ones). I know I've had a couple invaders that have been complete jerks.
Yes, forcing them to work the moment they are captured should also be a thing IMO. But I'd wager you would need to assign a guard to the room they are assigned to. Since removing their gear doesn't happen in this game, if they get free they'll just run rampent again.