The in-universe explanation was that the hospital created his department for PR reasons so that they could say they are the best at diagnosing stuff and so attract more patients even though most patients would just go to regular departments. The PR worked and so House’s department would often get transferred patients from other hospitals too, when they couldn’t figure out what was happening to them. Regular people would also seek out House specifically when they felt like they weren’t getting the right treatment.

But my interpretation of it was that the whole PR thing was just an excuse Cuddy came up with to help House. She knew what he was capable of but also knew he would never fit in on any regular job so she created something specific for him. She’s the friend every ADHDer or autistic dreams of having.

My interpretation was that he cares about solving the riddle in time, kinda like competing with the diseases to show he’s better. I don’t remember anything about him caring about the people specifically, except for a few specific patients that he liked.