Doctoral Advising: No Available, Appropriate Chairs
Even if it's not "distance learning", there is an obvious hazard in admitting doctoral students that do not fit into the capacity of the faculty. It's irresponsible to the point of immorality. Ok, but/and once they're in your program, yes, your program has an ethical and even moral obligation to serve them well.

There is the complication that, if the students are by-accident allowed to toooo freely choose topics, that it is manifestly infeasible to properly advise them. Someone "should have" explained this to them at the outset. In doing a PhD, "distance" or otherwise, one cannot choose a topic first, and somehow insist that the faculty in the immediate vicinity supervise it. (Nor, of course, is it sane to try to do a project independent of an advisor, or significantly outside one's advisor's expertise. It's hard enough to do a PhD project even when one's advisor is an expert on the topic.)