pshuang: nobody said it wouldn't make sense for the hotel to charge an early departure fee. However, it doesn't feel right to do so on a "Best Flexible Rate".
Best Flexible rates normally have no minimum stay requirements. You can define other rates for that and call them "Great rates", "Value Holiday" or whatever and put into the conditions that the rate is only valid for a stay of at least n nights -- if you check out earlier, the best flexible rate will be applied.
I also know of special "Weekend Rates" that apply if at least one weekend night is included. If the weekend night is the last night of your stay, and you check out earlier, you pay the normal rate (in particular, you pay for breakfast, which would have been included in the Weekend Rate).
An early departure fee simply leaves a sour taste, especially if the hotel does not offer a cheaper "Best flexible rate" with a minimum stay requirement.
HTB.