As generative AI becomes more prevalent in design, questions arise about which factors prompt design professionals to delegate creative tasks to AI-based systems. This study investigates whether a generative AI-based system for early-stage design can evoke inspiration, a critical driver of creativity, and how that inspiration influences the willingness to delegate. We conducted a scenario-based online study with 208 participants, measuring two components of inspiration (being inspired by and being inspired to) and their effect on delegation. A mediation analysis indicated that users who feel stronger inspiration from AI stimuli were more inclined to entrust the system with design tasks. These findings advance IS research by highlighting the importance of domain-salient factors such as inspiration as a vital factor that bridges creative engagement and delegation processes, informing how AI can be meaningfully integrated into phases of design.