I don't know if it's necessarily the case that ALL reassurance has to stop in order to get better, but rather I think it's important to be aware of the consequences of our actions. Whether we like it or not, continuing a habit of reassurance seeking is going to lead to more anxiety, just like a drink to an alcoholic could be the beginning of a major bender.
Learning to resist the urge to seek reassurance is a muscle like any other, and I think it helps when we know, eyes wide open, that making that doctor's appointment, or posting that question on the AZ, will give us TEMPORARY reassurance, but that soon we'll end up right back where we were before—afraid. That way, when the reassurance wears off and we're anxious again, we can look back and say, "well, that didn't really work, did it?" Over time, I think that knowledge alone can lead to better decision making, and the desire to seek reassurance becomes less and less once we realize it doesn't really bring the results we're looking for. This is how it worked for me, anyway, but it's a matter of working through that process—someone in the throws of HA, who IS addicted to reassurance seeking, would never believe that in order to feel better, they must completely curb that behavior. And that's the key—it's not about "forcing" it, it's about gradually getting oneself to a place where reassurance seeking is no longer even something we want to do.
Does that make sense?