When we say electricity is a "natural monopoly" what that means in the history of transmission utilities, states have stuck a bargain to grant monopolies in exchange for being tightly regulated, and so there's no version of reality where the state isn't already immersed in regulating them.

Every state in the country has a public utilities commission and they are constantly immersed in complex policy work from implementing legislation to working through an endless docket of cases that fine tune policy to specific tasked out responsibilities like getting a "standard offer". Sure it's complicated but I can't think of any reason that defaults to "don't regulate". We regulate healthcare too, and Medicare is always cheaper than private alternatives.

The problem with leaving private actors to their own devices when they have monopolies is that every conceivable grey area of judgment calls that impacts profitability will be subject to abuses of discretion, such as building out overpriced infrastructure, and investing in cheaper, unreliable transmission infrastructure instead of building for the long term.