One good reason for protectionism in this way is to protect from international shocks. If there was an event that caused international production of formula to scale back (say a volcanic eruption), then it would be beneficial to have as large a domestic supply as possible. This is achieved by subsidizing local production, eg via tarrifs on foreign imports. It would be valuable in addition to expressly allow for foreign imports in response to shocks like this, but making that the permanent regime would have its own risks.
How does consolidating an industry improve its resilience? Unless consumers have all decided that they love the formula exclusively manufactured under that volcano, they're not going to find themselves in the same bind that they are in now.
Now, this is different than if a certain country controls a significant portion of the raw materials needed to make a good, but that doesn't apply in this case. Cows and grass are abundant in every nation. Protectionism effectively reduces their supply, thereby increasing our exposure to shocks.
