The fuel would not go to the people that need it the most, it will just go to the people that can afford to pay the most.
Market allocations happen not on need but on liquidity. In that aspect it's fundamentally inferior to that other mechanism that distributes according to need and from ability.
Now, I'm not sure at what target your dismissive statement was aimed. Communism? Socialism? The phrase "From each according to their abilities to each according to their needs" is a phrase with long tradition, with some attributing the phrase to Morelly[2], so much earlier than the 'canonical' origins of socialism or communism. And the idea goes back much further than that.
But I'm not actually of the opinion that ideologies cause or solve problems. People cause or solve problems. Ideologies simply give people the justification for their actions. Most of the time people just do their stuff and find an excuse later.
Instead we should try to find ways to apply certain ideologies where they make sense. Want to develop an emerging market? Sounds like a job for some capitalism. Need to maintain a shared infrastructure? Pretty sure that socialism will create better results.
What we can see is that especially with indispensable goods and services, capitalism does bad job as soon as it comes to shortages.
[0] http://jpr.sagepub.com/content/13/4/343.refs
[1] http://www.amazon.com/Violence-Reflections-Our-Deadliest-Epi...
Yeah, that would be a pretty stupid system, I wholeheartedly agree. In situations where there's not enough supply to a indispensable good, rationing seems the only logical approach.
The UK has strict rules on how much petrol/gas anyone can carry. Consequently this type of law works as an automatic rationing.
https://www.manchestereveningnews.co.uk/news/uk-news/law-rul...
So yes, "allowing supply and demand to work" is a stupid idea that patently does not work at all, as exemplified by the ridiculous toilet paper shortage of 2020.