The total (monetary and nonmonetary) per-unit cost of a gallon of gasoline will be higher if the money price of gasoline is capped than if it is not capped. In short, price controls raise – they do not lower – the cost of acquiring goods and services whose prices are controlled.
It might still be the case that people who are especially rich in time will be better able to afford such price-controlled goods and services than they would if the price controls were abolished. (Although, for other reasons, even this possibility isn’t all that high.) But make no mistake: price controls meant to lower the cost that consumers in general pay for goods and services do the opposite: such controls raise the cost.