The settlement of the antitrust case (The Modification of Final Judgment or "MFJ" as it became known) occurred under Reagon's DoJ, but the case was actually filed under Carter.
Reagan might have approved of the anti-bureaucrarcy thrust of the break-up, but he probably had little or nothing to do with it.
In practice, it was the brain-child of Judge Greene, and it would not be fair to characterize Judge Greene as being anti-bureaucratic. The MFJ created a lot of nonsensical rules and line of business restrictions on telecommunications companies.
I'm not defending the Bells, and I'm not sure what the answer is. Some wanted a more aggressive enforcement of the UNE-P rules. Personally, I would have welcomed a further break up of the incumbent LECs, stripping the network elements out from service provision.
You are right to separate MCI from the criminal conspiracy known as WorldCom.
MCI, of course, was not all sweetness and light. The company was founded (with the encouragement of the FCC) to exploit opportunities created by regulatory inefficiencies. In the early days, they were known as a law firm with an antenna on top.
MCI could also act like a monopoly when it had the power. They were real tough in negotiating access to their Internet backbone before the merger with WorldCom.