How do governments factor elasticity of demand into their fundamental decisions on raising prices of petrol, diesel, or even alcohol, knowing fully well that most of these items are inelastic?

Goods like petrol and diesel have inelastic demands. Due to the scarcity of these products, the price of these products is usually high. If the price of the products with inelastic demand gets unaffordably high, consumer welfare in the country gets affected. To protect the welfare, the government bears the extra burden of scarcity. If the equilibrium prices are very high, beyond the affordable price, the government pays the extra price out of its own pocket.