This comes up every time people ask about billing daily. You're not billing hourly, you're billing daily, so the number of hours you work doesn't matter.
Some days is 4 hours, some days its 8 hours, some days it's 10 hours. Do more 4 hour days. You're probably only productive for the time period, anyway.
I like project billing, but the upside of time & materials billing is that your time gets a fixed valuation at the beginning of the project. Project billing puts you on the hook for things that come up unexpectedly during the project.
I agree with the value based pricing concept but I don't think it's _always_ effective for newer freelancers or larger projects.
For newer freelancers, it's important to be able to establish an hourly rate that meets your financial goals. For most, that would include a salary, expenses and then profit for your business. After you're receiving steady work at your base rate, you can start experimenting with daily billing, project based billing, increasing your hourly rate and so forth. But it takes time to get there.
For larger projects, there's inevitably scope creep and project based billing can be dangerous. I've been burned a number of times on large projects and now I put a "10% overage" clause in my estimates. If the time to completion is more than 10% over my estimate the project immediately jumps into hourly billing. It opens up a conversation very early on and sets an expectation that my work is not an open checkbook.
Of course! The great thing about project-based billing (in my opinion) is that it forces you (and your client) to come up with clear requirements at the beginning of the project, and anything extra is an additional scope of work. Of course if the requirements are unclear, hourly would be a better option.