I think one thing lacking in healthcare management programs that could potentially be met by the ACHE, is a formal mentorship program or "career education program". The sheer number of opportunities within healthcare is somewhat overwhelming to those new to the industry, and gaining a better understanding of career paths, potential jobs, etc. would be very helpful. Maybe student affiliates could specify an area of interest that they would like to learn more about, or even potentially job shadow, which could be something provided by ACHE at a local or national level.
While the responsibility ultimately falls to students and potential affiliates to reach out and build connections, having a built in system for making those connections could help students get started. If students knew they would have opportunities to meet those in their field as part of membership, they would be more likely to join and participate in the ACHE.