I think eventually you will not think this is as good of an idea as you do currently. There is a sweet spot for billing, just like anything else: somewhere between too often and too much. Just my 2p.
(1) The main advantage you get from setting your rate daily is that you will attract employers that see this as a way to eek more hours per day out of you. You can choose not to work with employers like this, but you won't actually know they will do this until they do it. In the end though, that is your time, and your rate goes down if you work more for the same amount.
(2) You will frequently work less than a day and charge for a day. This will of course keep some employers from hiring you, because they'll worry about your higher effective rate that what they would calculate for an 8 or even 6 hour day. But, let's say that they hire you. At some point, you'll send an email stating that you are done with the feature earlier in the day rather than later, because you have somewhere to be that night and don't want to forget, and then this puts the seed in their head that you didn't work a full day, and that for all they know, you may do that everyday with them if they aren't communicating with you all day to determine you are working for them.
(3) Although potential employers may attempt to do the math and convert what they perceive as your hourly rate based on your daily rate to what they get out of other hourly workers, much of the time, they won't want to bother. If anything, if I were trying to estimate your hourly rate, I'd divide your daily rate by 4 and assume that is basically your effective rate. And that is probably not right.
Then there is the whole thing about the perceived amount on your bill. It may seem higher if they see your daily rate vs. an hourly rate, even if it is less.
