One of the possible reasons that these Menorcan barracas are so tall is that the more gradual corbelling of the tall vault makes it all the more structural. A lower rounded dome shape (accomplished by cantilevering stones over the opening fairly quickly) would be less stable even though it would be less time consuming to build and use less material.
Another factor is the heat. Hot air rises and a taller ceiling would allow air inside the vault at ground level to be cooler. Crowded together under a low stone roof, sheep might still not be able to escape the extreme temperatures of the summer, unless the effect of their combined body heat was absorbed upwards by a generous expanse of large vaulted ceiling that these traditional barracas provide.
Are there perhaps other reasons why these structures are so tall?