Japan never had gas lines; America did, and resorted to rationing - people could buy gas only on certain days, depending ( if I recall correctly ) on one's social security number. The difference is that America fixed prices, Japan let the prices rise.
Yes. Gasoline had turned into an economic necessity for most people, and at that point a free market would have been even more disruptive than rationing. If less-than-twice-minimum-wage people can't get to work regularly, it's a worse problem than those same people waiting in gas lines in their spare time. The last-digit-of-license thing was a sop to show they wanted to make the lines shorter.
Why must you ignore everything which is known about economics? When prices rise, people make choices to reduce their usage. We have seen this in recent times, when gasoline prices went as high as $4 per gallon. People found ways to economize - travel a bit less, share rides, use a bicycle or scooter, buy a hybrid, etc. The government stats showed about 5% less gasoline usage as a result.
I don't disagree with any of this. What you are ignoring is that when prices rise dramatically, poor people economize by doing without, and and somewhat-poor people economize by mostly doing without. Somebody has to use less -- it's them, the ones who can't afford it. Some don't use much less but do pay much higher prices.
If for some reason the government wants those poor people to have some of the limited-supply product, they can get that by rationing. That's hard to organize ideally, of course, and poor people who get more of the rationed product than they think they need can sell their excess on the black market.
The classic example of this is famine. Throughout history, when food supplies got tight the poorest people starved. And they started starving while there was still more than enough food, because there was more profit in supplying rich people with more than enough of luxuries that wasted food than there was in selling to the poor.
When governments got organized enough to do rationing, they reasoned that they could reduce the starvation that way and get more citizens past the temporary shortage. If everybody gets enough to survive, that's potentially a good thing even if it means that during the famine there are no fat pigs for the richest.
In practice that only works for mild famines. When there just plain isn't enough food and some people have to starve, then one way or another the poorest people will die regardless. Their ration cards get stolen, they get killed and their ration cards used, the ration system breaks down and most of the food goes to the black market, the government picks the people it considers least valuable to itself and denies them ration cards, there are lots of ways for it to fail.
During WWI and WWII many nations that had food shortages tried to do food rationing and most seemed to feel that it reduced starvation.
It works best as a short-term thing, to help poor people survive economic shocks when the economy is far from equilibrium. The longer it lasts the worse it breaks down.
It's hard to confirm how well it actually works. Would the bureaucrats who operate the ration system do more good if they were put into the fields with hoes to grow food? At equilibrium, yes. For a sudden shock, it's hard to measure accurately.
Fixing the prices at artificially low levels prevented these adaptations from happening. This is what caused the shortages. There are thousands of years of examples of this process in many countries; it cannot be wished away by politicians or by people who prefer to ignore the laws of economics.
The oil shortage that Carter faced was caused by the revolution and various disruptions in Iran, followed by a lot of speculators hoping to make money fast. Sudden famines typically come from unusual bad weather. It's possible for a government to set things up so that there won't be enough food produced. In the most extreme case it could make farming illegal and kill anybody accused of farming. But when there is enough food 19 years out of 20 but this year there were heavy rains just before harvest and the grain rotted in the field, that might not have much to do with government.
And if you get a sudden shortage and wheat flour is $20/pound in December, that probably isn't going to get you a lot more wheat next season than if the price was only $5/pound. A temporary shortage followed by temporary rationing will probably not do that much to discourage farmers from farming.
You certainly have a point. I read that during WWII Nixon was a clerk in the price control office and he went through a time when no meat was shipped from Chicago to the east coast because the meat packers could not make a profit at the price they were allowed to sell. Maybe the war had gone on too long, and the government control was not flexible enough. Later Nixon phased in price controls and then phased them out again. I think maybe he wanted to show the public that he was trying to do something, and he couldn't think of anything else that would have such a visible effect.
There may be a better voluntary way to reduce the effect of big sudden shocks on poor people. If you can make a good argument for it, I expect a lot of governments would be interested. They get headaches from rationing that they'd likely rather avoid.