I inadvertently did a version of the "kindly brontosaurus" about 10 years ago. I was in my very early twenties, and about to go on my first trip abroad. The trip had two parts - first to one European country to visit a friend doing a study abroad, and then on a visit to a second European country to visit family. My immediate family was going to fly and meet me in the second country. Literally two days before my departure, my mom dug out my passport and we realized that it had expired. The closest place to get it renewed was at a major city 5 hours drive away. So my dad and I packed up and left super early in the morning, and went to try and renew it. We got there as soon as it opened (just!), submitted the materials and were sent to a room to wait. And wait. And wait. There was a woman behind bullet-proof glass, and when I got there I explained to her how this was an emergency for me, and any help she could give me was super appreciated, etc. Then I sat down. But I was wracked with anxiety, desperately hoping this woman would help me. I didn't do this consciously, but I kept my eyes on her the whole time and probably had my hands in a "prayerful" or "supplicant" gesture - because I was praying that every minute my passport would appear! Finally, I think she got a bit fed up with me (even though I was sitting across the room and on the other side of the glass), and she said "Oh, OK, I'll just go down and see if its ready." She came back, and it was!
Then, I literally had to race to the airport in major city, hop on a flight back to my home city airport, and then immediately get on the plane to my first European destination (just squeaked by before the boarding gates closed). If she hadn't given me my passport at that very moment, it all really wouldn't have happened.
So - my takeaway is that the kindly brontosaurus *might* be useful in those cases when the person really *does* have it in their power to help you, but they deal with so many people there is really no good reason why they should help you over other people. I don't think I could consciously choose to do it - my personality and demeanor probably wouldn't allow that unless I really was desperate and needed help.