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In many countries, the integration of growing shares of residential solar photovoltaics is beginning to challenge existing electricity systems. First, residential solar photovoltaics aggravates sharp system-wide load changes and, in turn, increases the need for fast-ramping generation capacity. Second, it reduces the demand for electricity provision from the grid, causing an increase in electricity prices as grid costs are recovered over smaller volumes of electricity. Battery storage (BS) mitigates the first integration challenge by flattening the system-wide load, but elevates the second by increasing self-consumption behind-themeter. In face of this dilemma, the integration of high shares of residential solar photovoltaics requires policymakers to re-design public support policies. In this article, we develop an agent-based model to simulate California's residential 'solar-plus-storage' market between 2005 and 2030 in four different policy scenarios. By applying a multi-technology, multi-policy approach, we quantify the complex interplay between the diffusion of individual technologies, several interacting policies and systemic challenges. Our results show that California's policy status quo initiated a BS uptake and, in turn, a flattening of the system, but, in the long run, will increase the electricity prices. To avoid this, we outline a policy reorientation-including a gradual phase-out of the prevailing feed-in remuneration and an introduction of fixed charges for owners of solar photovoltaic systems. Our results imply that the policy debate should be re-focused away from a single-technology single-policy perspective towards a system integration perspective. Neglecting this could not only jeopardize the affordability of electricity and climate change mitigation plans, but also put at risk the reliability of the electricity supply system. With investment costs of renewables expected to continue to decrease, this further implies that even countries without public support for renewables are likely to face challenges associated with their integration.