Large language models (LLMs) have enhanced conventional recommendation models via user profiling, which generates representative textual profiles from users' historical interactions. However, their direct application to session-based recommendation (SBR) remains challenging due to severe session context scarcity and poor scalability. In this paper, we propose SPRINT, a scalable SBR framework that incorporates reliable and informative intents while ensuring high efficiency in both training and inference. SPRINT constrains LLM-based profiling with a global intent pool and validates inferred intents based on recommendation performance to mitigate noise and hallucinations under limited context. To ensure scalability, LLMs are selectively invoked only for uncertain sessions during training, while a lightweight intent predictor generalizes intent prediction to all sessions without LLM dependency at inference time. Experiments on real-world datasets show that SPRINT consistently outperforms state-of-the-art methods while providing more explainable recommendations.