Many governments seek to improve population health, and some seek to reduce health inequalities. Yet, there remains a large gap between their policy statements and actual outcomes. Perennial questions in public health research include: why is this gap so large, why does it endure, and what can be done to close it? This essay uses political science and policy studies insights to address these questions, focusing on the distinctive issues that relate to (1) broad aims like 'prevention', (2) specific strategies for health improvement, or (3) new events. On the one hand, the idea of 'prevention' has widespread appeal, when governments think they can save money or reduce inequalities by preventing problems happening or worsening. While health protection seeks to inoculate populations against communicable diseases, health improvement strategies, including 'Health in All Policies' (HiAP), primarily address non-communicable diseases (NCDs). Further, the coronavirus disease 2019 (COVID-19) pandemic highlights the unequal spread of ill health, showing that preventive health ideas should be at the core of policy. On the other hand, there is a large gap between rhetorical and substantive commitment to prevention, a continuous HiAP implementation gap, and a tendency for COVID-19 health protection to overshadow health improvement. Explaining each problem clearly helps to identify the factors that generally undermine prevention policies and those specific to more detailed strategies like HiAP or events like COVID-19. We do not prioritise leadership or 'political will' as the policymaking problem. Instead, we identify the systemic factors that apply to even the most sincere, competent, and energetic policymakers. Health improvement policy is typically undermined by a lack of: clarity about what prevention means in practice; congruity between the prevention agenda (emphasising the need for major change to policy and policymaking) and routine government business; and, capacity to overcome obstacles to policy change.