The fine print in most programs state clearly that the benefits accrue ONLY to the FF account holder. While that doesn't stop a company saying you must use the points as the company directs, otherwise you will suffer the consequences, if you were to quit, they'd still be yours. Part of the reason for this term is that they want the flyer to do what is in the flyer's best interest, in terms of the FF program, as opposed to what is in the company's best interest. This may, and probably does, result in sometimes taking a more expensive ticket on a preferred carriers, as opposed to taking the cheaper ticket. If all the points "belonged" to the company, there would be no incentive for the flyer to choose any particular airline.

I don't think they would ever do it, but I imagine that an airline could collapse an account if they determined that the FFer had agreed that the points "belong" to the employer. After all, this would be tantamount to "transferring" the points, which is generally and explicitly dis-allowed.

For example, from the "Short Guide to the Canadian Plus Program":
Note that this point alone is highlighted in bold type, in the guide.

Regards,

Ken Hamer