Large language models have enabled sophisticated dialogue planning policy, but their reliance on LLM-generated simulation and feedback for policy optimization may introduce systematic preference bias. We present the first comprehensive analysis of preference bias in LLM-based dialogue planners, evaluating four state-of-the-art planning policies across three dialogue domains using multiple LLM families at varying scales. Our investigation reveals that all tested planners exhibit significant preference bias, systematically favoring narrow strategy sets rather than maintaining balanced distributions. User simulation emerges as the primary bias driver, while diverse persona simulation fails as an effective mitigation strategy. Most concerning, preference bias drives planners toward ethically problematic strategies that achieve short-term success while undermining real-world effectiveness and ethical standards. Our findings establish fundamental challenges for responsible deployment of LLM-based dialogue systems and provide crucial insights for developing more reliable and ethically-aligned planning approaches.