Questionnaires where they reveal things, often associated with at least a way to contact them for an interview, but sometimes with name and everything, usually is psychiatric settings (where people are often incarcerated without any proof, trial or any of that I might add). Things like whether they stole from their employer. Whether they ever used violence to obtain sex. They often ask children, homeless, prisoners, patients ... other groups with perceived or real precarious situations. (things that would never pass an ethical review board for, say, medicine)
https://onlinelibrary.wiley.com/doi/abs/10.5694/j.1326-5377....
https://ajph.aphapublications.org/doi/full/10.2105/AJPH.91.1...
https://psycnet.apa.org/record/1991-07467-001
https://link.springer.com/article/10.1023/A:1020007004436
So yes, I would say that a lot of people are willing to give up a LOT more privacy than a face picture for a small reward.
But the fact that that's true doesn't mean that people don't care about privacy.
You could even argue that it's indicative that people do care about privacy, as they attach a material value to it. This isn't an argument that I'm really making, but it isn't an unreasonable one.
