I think Oxford, CTC and FTE probably want a guarantee that if they invest in the assessment centers etc they get a return on that investment by having a fixed number of candidates at the end.
I know you pay the FTO for assessment but they are "supposed" to be a contribution to the costs rather than the actual cost.
I think it does make a difference which one you select. If Oxford had 33% more candidates then your chances go down by 33%.