I can find no historical example where government control of a resource resulted in a more efficient or 'better' use.
I know one historical example, Sweden in WWI and WWII.
In WWI, many basic commodities suddenly became scarce. Some businessmen were able to make lots of money from the situation, while other, particularly workers in cities were starving. There were ' bread riots'. At the end of the war, some rationing was introduced, but too late to have an impact.
In WWII the government had learned a lesson and rationing of basic foods and clothing was introduced from the start. You got coupons that entitled you to buy things like eggs, milk, bread, butter, with different coupons. The number of coupons depended on the number of people in the household. Underweight children got extra coupons.
Overall, the rationing system was perceived as fair. Certainly there were loopholes, like some produce escaped the rationing system and was sold on the black market. And city people with country relative might get some extra produce that way. There also was an extensive trading of coupons. As I understand it, just exchanging different types for coupons with someone else was legal, outright selling was not.
So although the rationing system in WWII did not work perfectly, it ensured that everyone got their basic needs met, and it was generally considered a success compared to the chaotic free market situation in WWI just 20 yrs before.
Btw, petrol was not rationed in the same way. It was just not available for ordinary citizens, but reserved for emergency vehicles and the military. Everyone bicycled for their daily travels. Actually, the army had a specialty: A big truck would drive with equipment, and the soldiers were transported by riding bicycles holding on to a long rope after the truck. A very energy efficient way of moving a large number of people.
Btw, less butter but no starvation and more bicycling made the Swedish population very healthy in WWII. Not that it was a happy time, with all the worries of a possible German invasion, no international travel opportunities, and all the horrible war news.
I was not yet born, but I have heard many stories from my parent generation.
nocar