Studies looking at electricity market designs for very high shares of wind and solar often conclude that the energy-only market will break down. Without fuel costs, it is said that there is nothing to set prices. Symptoms of breakdown include long phases of zero prices, scarcity prices too high to be politically acceptable, prices that collapse under small perturbations of capacities from the long-term equilibrium, cost recovery that is impossible due to low market values, high variability of revenue between different weather years, and difficulty operating long-term storage with limited foresight. We argue that all these problems are an artefact of modeling with perfectly inelastic demand. If short-term elasticity to reflect today’s flexible demand (-5%) is implemented in the model, these problems are significantly reduced. The combined interaction of demand willingness to pay and storage opportunity costs is enough to produce stable pricing. This behavior is illustrated by a model with wind, solar, batteries, and hydrogen-based storage, where a piecewise linear demand curve removes high price peaks and reduces the fraction of zero-price hours from 90% to around 30%, and entails more price stability for perturbations of capacity and different weather years. Furthermore, we show that with elastic demand, the long-term model exactly reproduces the prices of the short-term model with the same capacities. We then use insights from the long-term model to derive simple bidding strategies for storage so that we can also run the short-term model with limited operational foresight. We demonstrate this short-term operation in a model trained on 35 years of weather data and tested on another 35 years of unseen data. We conclude that the energy-only market can still play a key role in coordinating dispatch and investment in the future.