Hotel points for flying
 

Many hotels give airline points for staying with them, but I can't think of any airlines that give hotel points for taking one of their flights (in lieu of FF miles).

I would love to drop the 'odd' flight that falls outside of my normal accumulation pattern into Starpoints, for example.

Any ideas why airlines don't offer this (or do some)?

Airline mileage programs existed before hotel loyalty programs. In the '80s and '90s, many hotel customers desired airline miles, and hotels gave their customers the opportunity to earn miles to attract business.

The main reason airlines do not give hotel points is economic. Most American airlines are losing money, and they want to tie their customers to their mileage program. Hotel companies have been profitable and have greater pricing power than airline companies. Thus, they have more money (and willingness) to allow their customers to earn miles in lieu (or in Hilton's case along with) hotel points.

VS Flying CLub allows transfer of miles on a 1:1 basis with Hilton Honors. Minimum 10k then 5 k blocks. :p

AA allows miles -> Hilton Honors, 5K AA -> 10K HH. 5k minimum, blocks of 5K, now $25/transfer, so don't bother with piddling amounts.