It doesn’t provide direct relief to people without cars.
For sure. Hence mentioning car-dependency. I don't drive but everywhere outside of metro areas is car-country and there's no alternative.
Either way a shortage is impending and distributing based on price means the wealthier get more for often less than necessary purposes. Which is why I'd look for a different distribution mechanism, a need-based mechanism. E.g. rural transportation and farming should get more/cheap fuel, F150/RAM1500 commuters in the GTA should get less/more expensive fuel.