On a project that is non-billable and marked as overhead, how can Core stop entering time in the Client Hours column? Shouldn't there be time in the Hours column only?
Core marks automatically all the time entries as non-billable for overhead projects. The billable value of all time entries that are non-billable is zero, irrespective of the value in the Client Hours column. There is no way to turn that off in Core because it is meant to track hours in case they are billable. So the Billable flag is how Core determines whether or not to include them in the billing process.
The client hours are important because generally your employees have a bill rate and so you get an idea how much revenue you are potentially losing. Core uses the non-billable time value to report on some critical KPIs such as Utilization and Realization rates.