Comment by fcholf

I would also add that #SAT solvers, aiming at counting the number of solutions, are often implicitly solving the ALL-SAT in a more efficient manner than what you would have with modified CDCL solvers because they use other caching and decomposability techniques. Check knowledge compiler d4 for example https://github.com/crillab/d4v2 that can build some kind of circuits representing every solution in a factorized yet tractable way.