i don't understand all these time tracking apps to the seconds/minutes. as a consultant/freelancer don't you value your time and skills more than on the minute

i don't understand all these time tracking apps to the seconds/minutes. as a consultant/freelancer don't you value your time and skills more than on the minute at the desk working? how do you incorporate thinking about problems when your taking a shower or sleeping or the many other times you are not at your computer or desk without a timer and thinking. i find these can be some of the most valuable times there are for solving tough problems. ever since i started charging day rates, life has been so much easier. i set a minimum of 1/2 a day increments. 10x easier to manage, and it stops the client from looking at you as a cost center that they are loosing hourly on. it also stops the micromanagement of your time. estimating work is hard enough, tagging hourly on stuff makes it even harder. a day then can be as many hours are you like it to be. weather you end up working 12 hours or 4 is up to you and how well you get the work done. if the client is willing the pay the day rate for the problems you are fixing, the hourly time you spend no longer matters.