I'm sure others will chime in with actual experience on this, but I can think of a few reasons why they would not necessarily grant your request. Namely, the flight is overbooked for a reason: they plan for a certain number of no-shows/misconnects/cancellations. Thus, they won't really know if the flight is full+ until everyone is checked in and at the gate.

<edit: daggett24 beat me to it! >