Why would they need to conscript them? The Tower manages to find sisters to fulfil its ordinary functions - administrators, librarians, teachers - and they're not press-ganged into the work. Even if not every sister would be interested in doing a stint in a regional hospital, enough would be. And as the advantages to the Tower as a whole are so clear Sitters etc would be encouraging their Ajah members to volunteer, even if they disdained it themselves.
There's a similar logic behind opening schools and universities. The Brown Ajah would love it. I really think it just hasn't occurred to them.