Thinking back, every found-at-the-door convert (of which there were very few, could probably count on my fingers how many of them I saw) was either mentally unhinged or had just faced some life-altering event that put them at a low point. Death of a loved one, loss of a job and facing destitution, recent divorcee escaping an abusive relationship, drug addict wanting to recover, etc.
Other than that, the converts that weren't born-in were usually relatives that had been hounded by their JW family for years, sometimes decades. And more often than not, they were also at low point in their lives.