Large Language Models (LLMs) are increasingly used to simulate public opinion and other social phenomena. Most current studies constrain these simulations to multiple-choice or short-answer formats for ease of scoring and comparison, but such closed designs overlook the inherently generative nature of LLMs. In this position paper, we argue that open-endedness, using free-form text that captures topics, viewpoints, and reasoning processes "in" LLMs, is essential for realistic social simulation. Drawing on decades of survey-methodology research and recent advances in NLP, we argue why this open-endedness is valuable in LLM social simulations, showing how it can improve measurement and design, support exploration of unanticipated views, and reduce researcher-imposed directive bias. It also captures expressiveness and individuality, aids in pretesting, and ultimately enhances methodological utility. We call for novel practices and evaluation frameworks that leverage rather than constrain the open-ended generative diversity of LLMs, creating synergies between NLP and social science.