Proactive medical dialogue requires an agent to decide what to ask from incomplete patient information. Existing information-seeking approaches commonly prioritize questions that most reduce diagnostic uncertainty. While effective for acquiring informative evidence, this criterion overlooks an important property of medical diagnosis: different diagnostic errors can carry substantially different consequences. Missing a severe condition may matter more than reducing uncertainty among less consequential alternatives. Question acquisition should therefore consider not only how informative new evidence is, but also how it is expected to affect the downstream diagnostic decision. To this end, we propose Expected-Severity-Risk (ESR), a consequence-aware question-supervision objective that values each candidate by its expected reduction in severity-aware terminal risk. Because questions must be selected before their answers are observed, ESR marginalizes over possible answers using train-only population statistics. Its rankings are then distilled into a prefix-only language policy, so next-question selection requires no teacher-side computation at deployment. Across three Qwen3-4B training seeds on DDxPlus, matched ESR supervision reduces mean high-severity diagnostic miss from .0645 to .0455 (-29.5%) and improves mean diagnostic accuracy from .9123 to .9320 while requiring only 0.14 additional questions per dialogue. Fixed-budget analyses show that the two objectives remain behaviorally distinct when question count is controlled, while a matched expected-0/1-risk control shows that severity-aware weighting improves the high-severity error profile beyond generic decision-aware supervision. These results support moving proactive medical dialogue beyond uncertainty reduction toward consequence-aware evidence acquisition.

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