I think that the fact that people exhibit prudence is evidence for caring about many things that change in salience. For instance, if I'm driving home from work and I think "I need groceries, but I'm really tired and don't want to go to the grocery story," there's a good chance I''ll make myself go anyway. That's because I know that even if my tiredness is far more salient now, I know that having food in my pantry will be salient in the future.

I suppose you could model prudence as caring about different things in different contexts, but you'd need to add that you nearly always care about ensuring a high future preference satisfaction state on top of whatever you're caring about at the moment.