There is absolutly nothing wrong with donating anything that is yours, as the miles are. Taking a deduction for them is another matter, but it's certainly not illegal to donate them, indeed the airlines themselves have programs to donate the miles to charity.

As to why the airlines ask people to donate, it's the same thing as why a major company will put a canister out at their facilities for people to donate. People feel good when they donate, and they feel good about the company that makes it easy for them to donate. People will make a trip to a store if there is a collection box for a charity they like, and it may bring business into the store. Petco, for example, is currently offering you the opportunity to round up your purchase to the next nearest dollar with the change going to help stray animals. Petco can and does give money direct, but this will bring in the customers, they will purchase stuff, and feel good about donating.