Is there a name for the type of government where the government pursues consumer protection, antitrust, etc policy by directly running one competitor in every important industry, instead of making rules for every participant?

Not sure, but tbh that sounds like an efficiency nightmare.

I’d rather see governments rely less on private sector for things that make far more sense being under a ministry umbrella. For example - infrastructure construction and road repair. No incentive for quality roads if pvt company gets the annual contract