If you are going to pay the tab either way, open bar gives you a known set price. If you are going to pick up the tab anyway, and have them charge you by the drink you have no idea what your bar tab may be. You may wind up under the open bar price, or you may wind up way over it.
Lets face it, at the end of the day how do you prove they didn’t give out 500 drinks? Lot of room for some padding and fraud if you are paying the tab by the drink.
Reputable hotels, like mine, set the hosts down and give them a consumption sheet showing the amount of liquor, beer and wine that is stocked at the beginning for the function.
We then show the end of night inventory to them and compute the consumption based on that. All functions are separate and have separate liquor “cages” to control the inventory.
If something needs to be added (ran out of a beer brand for example) we have the hosts sign and approve a transfer sheet to show the added booze.