Some of what has been posted here deals with what rules and policies you impose. I agree that's critical, but it's independent of who makes the bookings.
As a consultant and a flyertalker, I of course like to make my own bookings (we do). But I have colleagues who do not. I also have colleagues who sometimes need help or advice - I know because they often come to me.
One other factor to consider is time. If your consultants are paid salary by you and then billed out hourly, do you really want them to spend their time on nonbillable travel planning, when a lower paid travel agent could do that for them?
Ideally, if you are large enough, the best solution is to offer your consultants a choice. Book themselves, or thru the company agent.