The low gas filling levels in underground gas storages (UGSs) in the European Union (EU), and the subsequent price volatility and geopolitical tensions between Russia and the EU triggered the adoption of counterbalancing policy strategies in the EU. A specific measure was the mandatory refilling of UGSs at 90 % by 1 November of each year to ensure adequate gas stocks. This paper assesses the impact of storage obligations on natural gas prices and the welfare of EU consumers for two market settings: a tight gas market, as experienced at the end of 2021, and a loose gas market. We use a gas market model with detailed technological constraints and uncertain input parameters. The uncertain parameters are sampled via the Latin Hypercube sampling method. The main sources of uncertainty are the storage settings, the scarcity induced both on the supply and the demand side, and the alternative storage targets. The results point out economic benefits mainly on EU consumers, in terms of avoided expenditures. The consumer payment savings under tight market conditions range up to 17 % on average, while the impact of the policy remains more questionable in the absence of scarcity: under loose market conditions, evidence of benefits is provided for 60 % of the simulated scenarios.