Most businesses do not replace manual timesheets because someone wrote down one wrong number. They replace them because payroll has become dependent on chasing, interpreting and re-entering information every pay cycle.
A manager may know that an employee stayed late, worked through a break or filled a higher-duty role. Payroll only sees what makes it onto the timesheet. If that context is missing, even a perfectly totalled timesheet can produce the wrong pay outcome.
That is the real value of a time and attendance system. It creates a clearer path from what happened during the shift to what is reviewed, approved and ultimately paid.