I like to feel that I'm spending my time productively, yeah. Not all of my time, mind you. People generally like to feel their work impacting their environment. Many consider it the most fulfilling part of their lives. Working purely for compensation is a great way to kill most positive energy for a solid half of your waking hours most days. People react differently, of course. For some the knowledge that they're making money alone provides the psychological reward, others find enjoyment in the moment-to-moment of things, even if they're not part of a meaningful goal, and yet others offset the meaninglessness of their work with a fulfilling home life or hobbies.

On the whole though, I'd say yes, people do care about productivity so long as they feel it's connected to their world and oriented in the right-ish direction.

I work remotely at companies until they fire me for doing the minimum. I still get paid for the two to three weeks, so I couldn't care less because the money goes towards my hobbies.