You are oversimplifying the halacha. Define “meaty”, and query whether a meaty oven of every definition always gives a pareve food baked inside it a din of meaty.
The reason for the issur of meaty or milky bread is that bread is commonly eaten at all meals and is normally pareve. This milky or meaty bread might thetefore inadvertantly be used with meat or milk.
The unique shape serves as a reminder that this is not like typical bread which is assumed to be pareve.