I think the main point from the company's point of view is that often the travel budget is not being spent economically. The risk with all of those points is that people book hotels, cars, flights where they get the most points personally and not where they get the best rate for the company.

I know of examples where 4 people from 1 company flew to the company's head office. They were all on the same flights to and from. What they did is they rented 4 cars (!) so that everybody gets his miles!

Nobody would behave like this if his own money was concerned, so as an owner of a (small) company I can understand ideas of companys regarding use of miles/points.