Traditional Business Process Management (BPM) struggles with rigidity, opacity, and scalability in dynamic environments while emerging Large Language Models (LLMs) present transformative opportunities alongside risks. This paper explores four real-world use cases that demonstrate how LLMs, augmented with trustworthy process intelligence, redefine process modeling, prediction, and automation. Grounded in early-stage research projects with industrial partners, the work spans manufacturing, modeling, life-science, and design processes, addressing domain-specific challenges through human-AI collaboration. In manufacturing, an LLM-driven framework integrates uncertainty-aware explainable Machine Learning (ML) with interactive dialogues, transforming opaque predictions into auditable workflows. For process modeling, conversational interfaces democratize BPMN design. Pharmacovigilance agents automate drug safety monitoring via knowledge-graph-augmented LLMs. Finally, sustainable textile design employs multi-agent systems to navigate regulatory and environmental trade-offs. We intend to examine tensions between transparency and efficiency, generalization and specialization, and human agency versus automation. By mapping these trade-offs, we advocate for context-sensitive integration prioritizing domain needs, stakeholder values, and iterative human-in-the-loop workflows over universal solutions. This work provides actionable insights for researchers and practitioners aiming to operationalize LLMs in critical BPM environments.