re: "We, as professionals, can use our own timers and brains for determining how many hours to charge."
Not every client wants the freelancers she hires to simply make up numbers.
Lots of clients find the time-tracker and work diaries to be valuable. It provides a rationale for trusting the billing from strangers ont the Internet.
As a freelancer, I consider myself to be a professional. I like using the time-tracker. I like not having to keep track of the time with my own brain, and like the fact that the screenshots show clients what I'm working on.