Public school choice has expanded rapidly across U.S. districts, yet most rely on centralized assignment with voluntary, opt-in participation rather than mandatory universal enrollment. We study the consequences of this design in the Los Angeles Unified School District (LAUSD), the nation’s largest opt-in system. Using two decades of administrative records, oversubscribed admission lotteries, and quasi-experimental changes in school access, we report four findings. First, participants are disproportionately advantaged: applicants have higher baseline achievement and are less likely to be low-income. Second, lottery-based estimates show a strong negative proximity-based gradient in achievement effects. This proximity-based heterogeneity cannot be explained by observable treatment effect heterogeneity, pointing to unobserved demand factors. Third, to assess the empirical relevance of the association between demand and causal effects, we estimate a structural model of application, enrollment, and achievement using policy-induced variation in access to schools due to large expansions in the public school choice sector combined with lottery-based admissions for identification of the outcome model. We find corroborating evidence for negative selection on gains and further highlight high application costs and weak demand as central frictions. Importantly, the vertical differentiation of public school choice programs, shaped in part by charter competition, generates meaningful potential for achievement improvements. Finally, counterfactual policy analysis shows that reducing information frictions modestly broadens participation, but mandating participation produces substantial achievement gains by expanding access and filling unused capacity at effective schools. Together, these results suggest that expanding choice options marks progress, but whether choice improves outcomes depends on the details of market design: voluntary, decentralized systems limit the promise of school choice, while carefully structured assignment mechanisms can unlock broader benefits.