The hours you work are largely irrelevant though. Your services are of high enough value to the customer to warrant charging per day. If you can provide the agreed upon service within 2 hours rather than 8, good for you. It doesn't matter to the client as long as they get what they pay for.
It of course depends on the work you do and so forth. If you are contracted by day for a job that require 8 hours of availability time, then you should probably work those 8 hours.
I think I see what you're getting at, but this seems like a circular argument. Yes, if the client is paying you "per day" and leaving it up to you to define a day, then of course they always technically getting what they paid for. Seems like if you really want to be paid based on output, you should negotiate a project rate. How else does it work? Do you and the client have to agree each day on the deliverables for that day?
