Branding isn't pricing power. If you see a McDonald's, you know what's in there. It may not be a premium product, but it's consistent, and consistency is worth something.

Buying a branded product is really buying two separate products. One is the commodity and the other is certification of the commodity by the brand. People might pay more for a product certified to be a known quantity than one that isn't, but that isn't the same as market power because certification can be a commodity too. Some random hole in the wall can't compete with McDonald's on being known and consistent, but Burger King and Wendy's can, which is sufficient to keep their prices in check.

Charging more because you're providing something some competitors don't have is not market power when some different competitors do have it.