The inverse may be true however. If you skip out 1 hour early every day but still accomplish a lot in your opinion, the company may feel that if you had stayed that one extra hour each day, over a week's time you billed them for a full day that they never received.

They may argue you could have accomplished the task 1 day early, saving them $X, etc.

I agree with your value proposition -- but I feel it's difficult to pull off in reality. I feel a lot more comfortable with billing Time and Materials rates, so basically if I skip out early one day, they aren't being billed for it, and the project goes on at it's pace.