The advantages as a freelancer for charging daily are clear to me from your posts, but what are the advantages for clients that make it a reasonable sell?
More importantly, there are many kinds of clients for which billing daily makes more sense. These also happen to be a type of client you'd really want to have.
Basically any large enterprise company that is used to paying a monthly salary to programmers, wouldn't even care about these things.
I would usually tell clients "We bill X per hour, billed daily at 9 hours per day, which comes out to X per day" or something similar. I would actually quote the hourly rate because, at least in my market, this is the way everyone immediately judges your cost (and value). (This also depends on what exactly you're selling - for extremely high-end freelancing work, I'd probably quote the final price, since I'd rather de-emphasize price and emphasize deliverables, but for basic programming work you will be compared to other programmers).
I haven't done it a whole lot, but I have negotiated a few development contracts on the client side. The very last thing on my list was how the supplier was going to bill us. I had a budget I couldn't exceed and the primary thing on my mind is "can these guys do the job on time and to the quality we need?"
The last time I did this I went with the supplier who was 3x the cost of the low bidder because I was more confident that they could do it on time. I have no incentive to save money (it's already budgeted for) and a great deal of incentive to not look like a fuckup.
Those are the 3 points of negotiation. Or rather 2 points. If a client is asking you to compromise on quality to reduce cost or delivery date, walk away.
So 2 points of negotiation. How much it costs and when will it be delivered.
Whatever you decide on the costs, make sure you can 100% deliver on the date agreed to. If you're late by even a day, you will ruin the relationship. That isn't to say they won't work with you anymore, but the relationship will become more difficult. It's as if you lied to them, however unintentionally.
Always deliver on time.
As far as how you break it down and bill them ... they don't really care. I bill by the week, day, hour, and sometimes by project ... whichever suits me at the moment or whichever I feel suits the client best.