I too had this same question. For a few months I didn't bother, and figured that a big controller with too many use cases was better than spending time rebuilding what was already provided. For whatever reason one night, I decided to build my own, and to not stop working on it til I at least had a character that could run and jump.
The learning process of figuring out how the transitions work and how the animation event triggers work, in addition to reading up on the ability code, really gave me a better understanding of the tools. Now I have some custom abilities that use custom animations and custom events, which AREN'T provided in the demo controller. Worth the effort if you want a random guy's opinion.
Actually, this learning process led me down a really deep rabbit hole, and I wrote a script which takes my rigged character, builds it in UCC using my custom controller, runs it through FinalIK to set up ragdoll, applies some other assets, and lets me go through the whole 15 minute process in one click.