In the back of my head I have always suspected that it's effectiveness
was influenced by how good you are at the particular remedy suplications that would cure the single affect. Like if you are better at cure disease, you will have a better chance of curing disease when you cleanse someone. Is this a totally mad theory, or is that maybe how it works?

I don't think it generally matters, however, healer edges can make this work this way. For example, being good at cure poison lets you pick remedy toxins, which helps cure poison but also helps cleanse cure poisons.