IMO cleaner waxes do more for polishing than for finishing. Mother's Pure Carnauba has more finesse in it than its cleaner wax (why, because the pure wax will not have (or isn't supposed to have) cleaning agents in it, and will have more carnauba content for paint protection. Mother's CG Pure Wax itself is a low content wax, but lets keep that discussion in another thread).
Nowadays, instead of tossing the cleaner wax, I use it as a go between from the finish polish, then the cleaner wax, then the pure wax (on my daily driver).
As an lsp, however, the cleaner wax doesn't do enough to fully protect and promote the paint. If you were to compare it between some other pure wax lsp's, the difference would be astonishing.