Speaking as someone who is in grad school now, even with prior research, the formal track of grad school is very helpful. I am doing research that I'm interested in. I don' t know if I'm a representative sample in that regard. It may be that people have more flexibility in math than in other areas. Certainly my anecdotal impression is that people in some areas such as biology don't have this degree of freedom. I'm also learning more about how to research and how to present my results. Those seem to be the largest advantages. Incidentally, my impression is that for grad school at least in many areas, taking a semester or two off if very stressed isn't treated that badly if one is otherwise doing productive research.