These fully homomorphic encryption systems can do boolean circuits, which are no more powerful than the arithmetic circuits you get with zk-SNARKs (in fact, are

These fully homomorphic encryption systems can do boolean circuits, which are no more powerful than the arithmetic circuits you get with zk-SNARKs (in fact, are an instance of arithmetic circuits). And with some zk-SNARKs, you get recursive composition, which lets you do arbitrarily many steps of a transition function expressed as a zk-SNARK, which is just as general purpose (albeit more involved) as applying a bunch of boolean circuits to some data.