Ironically, I spent six years in the USAF (2004-2010). That's how I ended up in Alaska. Just a regular enlisted POL guy--I wasn't uniquely talented enough for any of these exclusive extracurricular activities, so I don't have any firsthand knowledge of how those programs work.
I personally don't care that Uncle Sam pays for military personnel to play softball (or run track & field, or do any of that All-AF/Army/USMC team type stuff). I understand that the money spent on these Permissive TDYs is a drop in the bucket compared what they waste on other stuff. I just fail to see the point in having these programs--do they actually contribute to any unit's mission?