I am currently thinking about pursuing a public policy PhD after my MA is completed. One of my top target schools employs a visiting professor who has been at that university for the past several years. The main reason I wanted that particular professor is that his previous background included posts at several very high-ranking positions within the US government that I feel like would be helpful to me throughout my doctoral education and with the potential dissertation. But I'm worried that as a visiting professor, he'd make for a poor choice as a supervisor due to him being "visiting" instead of a more permanent professor at the school (is it?).
Most universities have PhD candidature rules that require the primary supervisor to be a permanent faculty member of the university. Visiting professors can sometimes act as co-supervisors, but you would need a primary supervisor from your university. This is done to reduce the risk of supervisor-loss.