That was the theory. Cut to practice: the first consequence of deregulation was the elimination of potential competitors, in an orgy of mergers and consolidation (not least because of the overly leveraged buying spree that ultimately left Worldcom in bankruptcy, as the FCC looked on, bemused). At the same time, the phone companies used their connections with overly friendly regulators to whittle away at the access requirements for competitors until some might have wondered if they even existed any more.
Well, soon they won't. The FCC, under Michael ("Colin's kid") Powell, is proposing to let incumbent local phone companies charge anything they like for access to their local wires, allowing them to price their competition out of the market. Which, when achieved (most likely; the FCC listens only to industry leaders on these matters, and which of them will oppose it?) will mark the transition of local phone service from a regulated monopoly, to a monopoly which can screw its customers however it likes.