I've been in these time card reporting situations on both sides. The information is very valuable to managers especially if clients need to be billed for appropriate amounts of time spent on work or just to understand what projects are consuming the most time. But managers are never able to understand the overhead required, or that the data they get is often a rough guess. (Edit: I should say 'managers are sometimes unable to ...' rather than never able'. Don't want to be unfair to managers...)
I got annoyed at a manager who was asking me to do time reports when I knew full well he wasn't even looking at them. So I just stopped submitting them. Took him almost a full year before he noticed, at which time he told the rest of the staff to stop doing them.