I see. I mostly agree, though I definitely think the delineation problem is more difficult with vertical rather than horizontal monopolies, e.g. (to stretch the example), McDonald's franchises currently cook all the food they sell. They could instead buy pre-cooked food from a separate business, but would such a breakup of functions benefit the economy? Where that line is seems like a hard problem for a court to solve.
mcdonald's is actually a good example. it's at least 3 businesses on top of the nominal one of fast food: franchising, supply chain, and real estate. franchisees pay for access to the mcdonald's brand, trademarks, and shared marketing. in addition, mcdonald's corporate provides complete supply chain support, so franchisees buy all of their food and materials through mcdonald's itself or from its approved suppliers. mcdonald's corporate also owns the real estate that many franchises sit atop, so it's a landlord to boot.
it'd be easy to split those businesses into separate ones, as it's plainly obvious that all three businesses can viably stand alone, apart from serving fast food. you might argue that that'd dilute the brand value because the product wouldn't be as uniform, but you just have to look at the international variation to realize that that's not so important to brand value.