why stop it at 15 minuites? I can't imagine a single scenario where splitting time reported into anything less than hours would matter all that much, and the best possible systems would be more freeform in approach, allowing the worker to specify the actual time they started and stopped, rather than only being able to start and cease work in specific intervals. It would allow for greater resolution naturally where the worker is switching tasks more often.
As for people saying such a system would be misused or completed lazily, those arguments apply equally well to filling out timesheets at all. I don't imagine anyone ever recorded themselves slacking off intentionally on a timesheet.