I used to work for Pepsi-Co so I am well aware of how their distribution works.
But in this case, at the point of retail it makes no difference. The store can sell as many different brands as they want. The problem is not the middlemen, it's the exclusivity arrangements that disincentivize brand competition.
Unfortunately the soda business isn't free of noxious exclusivity deals either. Restaurants almost never have both Coke and Pepsi products, it's either one or the other. As I understand it that's because restaurants get a lower price if they agree to exclusively offer one brand.
One of my dealers locally sells both Ford and Chevy. It's great for cross shopping. There can be exclusivity arrangements, sure, but it's not set in stone. And in any case Coke & Pepsi absolutely have the same sorts of arrangements with both retailers and restaurants.
Usually, your soft drink is manufactured from the brand's syrup by a bottling partner, which is then distributed to a retailer, who you buy it from.
e.g: https://www.coca-colacompany.com/content/dam/company/us/en/a...