Usually Gibbs is used when there's no directly straight-forward gradient (or when you are interested in reproducing the distribution itself, rather than a point estimate), but you do have some marginal/conditional likelihoods which are simple to sample from.
Since each visible node depends on each hidden node and each hidden node effects all visible nodes, the gradient ends up being very messy, so its much simpler to use Gibbs sampling to adjust based on marginal likelihoods.
"Is Human Behavior Just Running and Tumbling?": https://osf.io/preprints/psyarxiv/wzvn9_v1 (This used to be a blog post, but its down, so here's a essentially identical preprint.) A scale-invariant control-loop such as chemotaxis may still be the root algorithm we use, just adjusted for a dopamine gradient mediated by the prefrontal cortex.
"Give-up-itis: Neuropathology of extremis": https://www.sciencedirect.com/science/article/abs/pii/S03069... What happens when that dopamine gradient shuts down?