I'm nearly certain that saving on quantity is not the reason. If there is a cost reason it could be that having 2-3 soda machines per club is more expensive than having 1-2 both from a capital cost and a maintenance standpoint. The actual cost of the soda is so negligible that the labor to distribute it manually is certainly more.

It goes with the aesthetic to not look like McDonald's lobby with public soda fountains, it goes with the service ambience to have staff dispense it since they need soda anyway for their mixed drinks.

The cost of a fountain soda is roughly $0.12 per drink. I have no doubt that those cookies which taunt me or the pimento cheese I can't stop eating in the ATL clubs costs more per serving.

The iced tea costs roughly the same and is freely available but that's because it looks classier in a glass container and the bartenders don't need it.