I am not sure exactly what you mean when you say there is a push for a member-driven organization, but I assume that you mean that the members should have the right to elect and remove the board and have ultimate control over the organization.

In my view, there are a limited number of situations in which a membership organization makes long-term sense for a nonprofit organization. Those situations generally involve members who fully care about the organization, are sufficiently involved to pay attention to its governance, and have a personal stake in the outcomes.  These include groups like homeowners associations, neighborhood associations interested in local zoning issues, social clubs, trade associations, and some kinds of churches where the congregants appoint the clergy.  Membership organizations are also good for a parent organization controlling a system of multiple agencies or for the sole-member/founder who wants to assure the right to fulfill his or her dream. 

I don’t think membership organizations are normally good when the members are merely users of the services, like hospitals or arts organizations.  I am particularly concerned about membership organizations when the organization controls significant assets that could be taken over by the members and diverted from their original purpose.  Groups like museums, which are holding artifacts for all posterity, should not be controlled at the whim of current members.

The directors of a nonprofit corporation have a fiduciary duty to the organization to assure that it fulfills its mission.  Members do not have a fiduciary duty to the organization and can act solely in their own self-interest.  Giving the members control may make sense when their direct and collective self-interest is at stake, but usually not otherwise.

Your organization could be close to the line if it is a specialized service that deals with a particular disease where the patients have a collective interest in the type of treatment or service.  If it is simply a general health clinic for anyone who needs medical help, it would seem less appropriate to convert to a membership organization.  You can do a lot with advisory boards, patient surveys and other devices to obtain input with regard to the facilities without giving over control to those who are merely passing through.