That's all well and good @Theodore Baggins, and I would agree with you. However, a 2017 study from The University of Texas at Austin showed that over 90% of zombies do NOT have the actual capacity to process fat from their eating of human brains. This is explained due to the fact that most zombies no longer have a "proper" digestive track that would allow the processing of fatty acids. The study took on 124 specimens, and amongst these only 9 had a digestive system somewhat capable of taking in fat. So that's nearly 93% without this ability. Furthermore, 7 of those 9 specimens were morbidly obese zombies, aka "Brutes". And as you may well know, they are no brutes on our lovely island (they just can't make the swim).
So yes, brains do contain fat, but the friendly zombies on our roads, in our forests and on our beaches cannot absorb it.
Sorry @elroy.