I found the conversation towards the end about pricing yourself per hour as amateurish really interesting.
I have been freelancing for about 10 years and I think because I'm just in a slightly different field it is different, but I have never heard of a day rate before Jake Parker, and I have TRIED to request a flat rate a few times, but my clients always want an hourly one instead haha.
Personally, I always give an hourly rate with an estimated amount of time I expect the project will take, and updates on how much time I've used when I turn in roughs etc. and especially if I think we will go over I let them know as far in advance as possible.
When I do "commissions" like a painting of someone's family I do those as a flat rate. And when I've done self published books as well, but when working with a larger company or client I do hourly. Not sure if that's just because my clients have been in a different industry, such as games or video production or marketing. But I'm always asked upfront for an hourly rate and have been told specifically that my client prefers that over a flat rate.
Anyway I think it depends on the field you're freelancing in! 🙂