A written policy is best, if you can get a good one!
Several years ago, I became embroiled in the issue of frequent flyer miles and bumping compensation. It took the better part of two years to finally get the local government involved to adopt a written policy. All of the while, indignant taxpayers were writing letters to the editor and the local newspaper even weighed in by railing that all miles and compensation should accrue to the municipality.
One of biggest myths out there is that these miles can be pooled, which is not the case. As a practical matter, administering such a program is not only time-consuming, but it necessarily involves gross violations of privacy to separate personal travel from "official" travel. There are gray areas, too. For example -- and no thanks to a local government that may fly me somewhere once a year -- I receive substantial mileage bonuses through my elite status and by registering for various promotions. Should ALL miles from the occasional trip be cordoned off for future use by the government entity? How long should a person be expected to keep track of that? Should my personal FF account be subject to the open records law? I certainly don't think so and like me, the great majority of travelers who would be subject to such a policy might never accumulate enough miles on official business to equal a free ticket in the course of an entire career. (Think about members of citizen commissions and part-time elected officials who are essentially donating their own time to attend training or meetings or a high school kid who attends a leadership meeting on behalf of the municipality.)
The bottom line: in most cases, the travelers were being asked to give up something that could be of some value to THEM, but the value that would potentially be recoverable to the organization is far, far less. Most affected miles would expire worthless, along with the occasional non-transferable bump vouchers (VERY occasional, since who is going to take a voluntary bump, inconveniencing themselves, families, etc. for nothing?)
After a long struggle, we ended up with a policy that -- SURPRISE! -- echoes the airlines' own policies and practices. Miles and other compensation belong to the traveler, period. People who travel on business are expected to act in a manner that does not diminish their ability to perform the business, which means showing up on time for their meetings and showing up in their offices following the meeting (or using personal time off to cover, if it doesn't inconvenience anyone.)
The experience here applies to non-governmental employers, too. Much mischief and political hay can be made by and with people who don't understand FF programs and bumping. Some of it revolves around ignorance or just pure jealousy that someone else might be getting something. Mix all of that in with the sometimes petty nature of some people and you have the makings of loud discussion that is much ado about almost nothing.
If there is an opportunity to adopt a thoughtful, written policy in an organization that avoids all of that non-productive discussion and accurately recognizes the realities involved in business travel, that is the very best solution. If the outcome is more likely to be engraving a Draconian policy of ignorance and injustice into stone so somebody can pose for holy pictures next to it while diminishing employee morale and never producing any substantial value to the organization, then I think some questions are better left unasked and people are best left to their own devices.