As noted by Kleb, above, the number of amateurs is the critical point. This is particularly true for the discovery of moving objects, such as comets and asteroids, which historically were found more often by amateurs than professionals; and even now, since any serious amateur can spend hours poring over the immense image databases available online, some of the most interesting objects found in any given time frame are found by amateurs. In my case, my main topic of study is the history of the New General Catalog, which is not the sort of thing many amateurs are interested in; still, every now and then I receive a note from an amateur who stumbled across my site, pointing out a numerical or other typographical error in the work I've posted so far, and since without that free editorial commentary, I might never have noticed the error, I'm very grateful for their help.
In my specialized field of exoplanets, I can say that these two are now much closer and are doing important work together. For example, in the Next-Generation Transit Survey (NGTS) project, we can see a large number of Let's see amateur astronomers and astrophysicists who are doing projects together.