She's still a princess, there's a clear and evident divide between Rose and the common folk. The social divide would cause scandal, that scandal would not be able to be kept under wraps because it would be the literal sovereign ruler of the nation fucking around. Even if that wasn't the case, do you honestly think the Duke would let her? 7.0 has a flashback that gives him a reason to be as greedy as humanly possible, he's not going to want to share.It is implied that in the town/city almost all the inhabitants except the protagonist and the children end up in something similar to Sodom and Gomorrah, the people are already so corrupted that they see no decency or moral sexual acts.
Quietly everyone can end up fucking her and not tell Leto for that reason, and also for plot convenience, although it can be perfectly real because there are people who have so much bad luck that everything goes wrong (i'm almost one of those xD).
Also I think you might be exaggerating the state of the city.