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This research paper evaluates the role of green hydrogen in residential heating and power-system decarbonisation across the EU-27, the United Kingdom, and Switzerland between 2025 and 2050. Using a bottom-up reconstruction of residential heat demand, Monte Carlo uncertainty analysis, and least-cost optimisation, it assesses hydrogen through levelised-cost, merit-order dispatch, and investment-viability tests. The results show that heat pumps and district heating form the cost-optimal decarbonisation pathway, while hydrogen has only a limited role in direct heating but can provide value as a dispatchable low-carbon peaking resource, subject to appropriate capacity-remuneration mechanisms.