Problem reframing is a designerly activity wherein alternative perspectives are created to recast what a stated design problem is about. Generating alternative problem frames is challenging because it requires devising novel and useful perspectives that fit the given problem context. Large language models (LLMs) could assist this activity via their generative capability. However, it is not clear whether they can help designers produce high-quality frames. Therefore, we asked if there are benefits to working with LLMs. To this end, we compared three ways of using LLMs (N=280): 1) free-form, 2) direct generation, and 3) a structured approach informed by a theory of reframing. We found that using LLMs does not help improve the quality of problem frames. In fact, it increases the competence gap between experienced and inexperienced designers. Also, inexperienced ones perceived lower agency when working with LLMs. We conclude that there is no benefit to using LLMs in problem reframing and discuss possible factors for this lack of effect.