One reason cards set it up so you charge your card in the normal way and then pay your card bill with points, rather than paying for the meal with points, is employee expense reimbursement.

If you get a normal bill for business expenses, you can get reimbursed. How you pay your credit card bill later isn't anyone's business but your own.

If you were to use points to pay for the meal directly, you would often not be eligible for reimbursement. (Showing the itemized check that you get before you pay wouldn't do, since it doesn't identify the diner. Anyone can pick up any number of itemized restaurant checks easily. Corporate expense accounting people know this. They also know that the itemized check you find on the floor can be for twice what your meal cost.)

This doesn't benefit everybody, but it doesn't harm anybody either. So, an upside for some people, and essentially zero downside.