A good point that one or more people have brought up is the infeasibility of managing all these frequent flyer miles for government use. You'd have to hire people to manage the frequent flyer miles, and it might turn out that the cost of sorting through them for "official use" isn't worth the cost of hiring the person to do the sorting.
I have a friend who works for a company (not the government directly) that uses government-established per diem rates as their guidelines for what employees should spend for food and lodging in a certain city. They used to require that employees collect all their receipts, including meals, and submit an expense report at the end of the trip. Then accounting would go over things, double-check, do whatever paperwork they needed to do, etc.
Well, when they looked into it, this was costing them a fair amount of money. By requiring that the employee deal with so many different receipt, and itemize down to the penny ("here's the 7-11 receipt for the 72 cents I spent on a Coke, and..."), the time to prepare an expense report was astronomical, relatively speaking. And then accounting had to put in just as much time.
What they ended up doing was going to a system where employees didn't have to itemize lodging or food costs unless it went over the published per diem rate -- and then they had to justify why this was, maybe get approval, etc. But if they were at or under per diem, they just said so and they got reimbursed the full per diem amount. If they were 10 bucks under per night on their lodging, good for them. They earned an extra 10 bucks that day.
In the end, it's saving his company money since people were paying reasonably close to per diem anyway. Expense reports can be done in 10 minutes, instead of an hour. Accounting isn't trying to cross-reference everything. You save the labor hours at whatever overhead rate the company has. And usually employees net a few extra bucks per day because they come in slightly under per diem. It's a win-win situation.
Now, granted, there are employees who try to make a profit on this. My friend stays at a friend's house whenever he goes to one particular city, and nets the whole hotel per diem for his own personal income. But, eh, so what? Before he stayed at per diem hotels, it's the same cost to the company, he's inconveniencing himself (and his friend) to make 100 bucks a night, which is worth it to him. Everybody's happy.
Anyway, this has kind of strayed off topic. Just reaffirming that sometimes the cost of dealing with things simply isn't worth it, and letting employees (even government employees!) have an extra perk is actually a win-win situation. Besides, much as it might make some people cringe to think about it, when you're talking about hundreds of millions or more dollars in Division X or Project Y, the cost of a $800 plane ticket is down there in the noise.