If you bill daily, and waltz in around 10am when the company has been open since 7, and then waltz out at 2 when they stay till 4... it may be a little challenging to convince anyone that you really accomplished a full day's work ("well, if you had been here that extra few hours, we could have gotten X finished today", etc...)
Nobody said when you charge daily/weekly you get to slack off. You absolutely have to deliver the value if you want to keep getting contracts and referrals. Billing daily or weekly helps to refocus the discussion from a metric that people very commonly attempt to micromanage and pick apart (hours) to a metric that actually benefits the client: the ROI of your services. Who cares if you worked 15 minutes extra on Tuesday and left 10 minutes early on Thursday when you can show to your client that your ROI is 300%?
When I leave at 3 in the afternoon because I'd like to pick up my kids from school for once, I'm not "slacking off", but I'm definitely taking time that could have been employed productively, so I don't think I would feel good about charging for a full day. When I stay until 8 to fix something, I kind of want to be reimbursed for the extra time I'm putting in.
You spent time on their stuff that day instead of working on something else or some other client. The opportunity cost to you is the same, whether you leave at 3pm or work until midnight. Charging by the day or week allows both you and the client to not think about low level implementation details like that.
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.
If you end up working out of their offices and on their schedules, you're already blurring the line about being a contractor in the first place. More like a temp really.
