Billing hourly or daily is about the same. Weekly gets complicated. It is all about reducing risk, locking in cashflow and getting compensated for your time and energy.
Weekly/Monthly billing means you can never take a vacation. And if you're going to suggest pro-rated weekly billing well that's just daily or hourly billing isn't it?
You could certainly take week-long or month-long vacations, or take a month off of consulting to do things like business development or education. Generally, if you're at the level where you're billing engagements weekly or monthly, monetarily you don't need every single week to be filled with billable work.