If you need to find where you are after steps, a general graph requires simulation. You would visit each node one by one for steps. With functional graphs, you can precompute structure and answer in time. If you need to detect cycles, general graphs need hash sets and careful tracking.
You might miss cycles or count wrong. Here, cycles are guaranteed and have special properties you can exploit. The constraint creates opportunities for faster algorithms. Every problem on functional graphs has techniques that do not work on general graphs.