Goodness, I would hate to have to log in and do that daily! Plus, it wouldn't really be putting everyone on equal footing.
While that would, in theory, give everyone the same chance, in practice it would greatly advantage those who live in Eastern or Central time zones and have free time in the morning. I personally would be screwed because I have to start work at 7am, and I don't have even 10 minutes free to make Fast Passes at the start of my shift. Its's not practical for me to take off a week so I can get my Fast Passes in the morning, and people who live on the west coast would have to get up and be online at 4am for days on end.
Secondly, some people would have faster internet, faster equipment, and faster fingers. Some people would 'win' the coveted Fast Passes, and others would still lose out. It would be a mad scramble every morning, and Disney's stellar IT would lead to lots of headless Olafs. I'll gladly take one day of possible frustration over several in a row.
I also think that your premise that this would allow people to avoid arranging their days based on Fast Passes is flawed. The current system advantages those with longer stays, so people generally CAN get the coveted fast passes later in their stay. With a daily FP booking there would be some people who "win" at the fast-fingers race every morning and others who would "lose" it for every single day. So instead of planning your trip once with a thought for AK on day 5 for FOP, people would be adjusting plans daily based on what they can score. Instead of being able to get SDD or FOP for day 5 of a trip, some people would end up not being able to get it at all, even with a long stay, while others would scoop up what they want for every day.