I check out at the front desk for several reasons:

1) There are usually charges (phone calls, breakfast, minibar) which are not on the bill slipped under the door. I need the final bill to be reimbursed fully by my company.

2) I confirm bonuses that I am entitled to (GP, UA, etc.) It is often not enough to ask for this at checkin.

3) It rarely takes me more than 2 minutes to check out at the front desk. If I have to call for a copy of the bill, it requires considerably more time and effort on my part. If I didn't get the bonus credit, it would also take a lot of effort on my part to get it posted.

4) Checking out clears the room for maid service, and a guest who may be arriving early. It is considerate. And technically, I suppose you could be charged if you don't officially check out at the published time.