Politeness is a core dimension of human communication, yet its role in human–AI information seeking remains underexplored. We investigate how user politeness behaviour shapes conversational outcomes in a cooking-assistance setting. First, we annotated 30 dialogues, identifying four distinct user clusters ranging from Hyperpolite to Hyperefficient. We then scaled up to 18,000 simulated conversations across five politeness profiles (including impolite) and three open-weight models. Results show that politeness is not only cosmetic: it systematically affects response length, informational gain, and efficiency. Engagement-seeking prompts produced up to 90% longer replies and 38% more information nuggets than hyper-efficient prompts, but at markedly lower density. Impolite inputs yielded verbose but less efficient answers, with up to 48% fewer nuggets per watt-hour compared to polite input. These findings highlight politeness as both a fairness and sustainability issue: conversational styles can advantage or disadvantage users, and “polite” requests may carry hidden energy costs. We discuss implications for inclusive and resource-aware design of information agents.