No, the US government didn’t distribute gasoline. Some state governments issued rationing regulations in one or both of the oil crises, and the US government imposed price regulations during part of the latter of the two crises.
What the DOE did was allocate a gas allotment to each gas station. Stations individually had to apply for gas allotments. If they ran out, too bad. If they had too much, they couldn't allocate it to another station.
The result was shortages and gluts. The DOE proved completely incapable of adjusting to constant shifts in demand. They'd allocate based on the previous year's pattern.
So we learned.
> Distribution of mail, especially to the last mile routes that aren't profitable, does.
UPS seems to do it just fine (for packages), at a profit.
Let's look at something simpler. The US government has proven itself inept at distributing gasoline, which it did in the 1970s (as in long gas lines in some areas and gluts in others). The oil companies, before and after, have been remarkably adept at providing plenty of gas for anyone who wants to buy it, despite refinery explosions, pipeline disasters, etc.
Before government got in the US healthcare system, the system worked well and costs were reasonable.
Internet services run by free market companies seem to be remarkably not brittle.
> "efficiency" often means ignoring maintenance needs.
The government has been ignoring maintenance for decades. The Seattle government ignored the bridge maintenance while they blew through all the money on various progressive causes, and now the bridges are shut down because they're not safe to drive on.
Government run farms have never in history been able to feed a country. The free market farms in the US fed the US and the USSR. (Kansas wheat was exported to the USSR that desperately needed it.)