Artificial Intelligence Impact Assessments ("AIIAs"), a family of tools that provide structured processes to imagine the possible impacts of a proposed AI system, have become an increasingly popular proposal to govern AI systems in the US and EU. Recent efforts from government or private-sector organizations have proposed many diverse instantiations of AIIAs, which take a variety of forms ranging from open-ended questionnaires to graded score-cards. However, to date that has been limited evaluation of existing AIIA templates.We conduct a preliminary classroom study (N = 38) at an R1 university in an elective course focused on the societal and ethical implications of AI. We assign students to different organizational roles (e.g., an ML scientist or product manager) and ask participant teams to complete an AI impact assessment for two imagined AI systems and deployment contexts. In our thematic analysis of participants' responses to post-activity questionnaires, we find a consistent set of limitations shared by several existing AIIA instruments, which we group into concerns about their format and content, as well as the feasibility and effectiveness of the activity in foreseeing and mitigating potential harms. Drawing on the findings of this study, we provide recommendations for future work on developing and validating more effective AIIAs.