You give up the notion "if <thing I don't prefer is the case in the universe> then <I must make myself sad or anxious or offended>".

Right, so I think what is being missed here is the functional role sadness, anxiety and offense play in motivating human action. Sadness has intensionality - it is about something - and its proper role in a human mind is to motivate various complex responses along the lines of "avoid this" or "prevent this from ever happening again." Lose the sadness and you lose the motivational power it contains. I don't think this motivational power is actually replaceable by a more generic abstract preference. (Or else charity fundraising would just say "we offer 20 utilitons per dollar" and that would be enough.)

Of course, the kind of emotional distancing recommended here might be necessary if the sadness/anxiety/offense actually becomes, in itself, an obstacle to achieving your goals - which can certainly happen. But it is not the general case.

EDIT: Just to be clear, I am talking descriptively about humans, not prescriptively here. It's too bad that we aren't strongly motivated by "20 utilitons per dollar." We should be! But we aren't.