Other than a kind of cool hobby, what are the advantages of casting your own bullets? I have made my own jig heads for years for fishing but obviously the tolerances on a fishing jigs and a bullets are not even in the same class. With all the bullets available and the quality control that goes into it I'm puzzled.

I would be afraid mine would shoot around corners!
Yes, just about any bullet you can imagine is available from several sources--many sources in most cases. Don't assume there's necessarily any quality control, however. I think it's fair to say that if the source has been in business for a good while and you know many shooters are using their product, yes, the quality is probably there. Just don't assume it's any better than what you can produce yourself--it probably isn't.
No need to be afraid--it's not rocket surgery and there's an amazing amount of tolerance inherent in the system. In learning, I've made many dozens of ugly bullets that weren't cast very nicely, didn't size very well, and some that even got damaged in handling. In the cases where I chose to load and shoot them, they hit the target just as accurately as the nice ones did. You'll learn quickly...it's not difficult, and there's plenty of folks here who will help you to produce bullets the equal of anything you can buy in short order.
The short answer to your question, for me, is cost. I couldn't possibly afford to shoot as much as I do if I bought bullets of any kind. The savings is substantial, and I don't even scrounge anything--I buy my lead off eBay for $1.15 to $1.25/lb shipped, and that produces 25-30 bullets (255 gr). As for time, I can produce 1,500 bullets in two or three evenings' work--cast, sized and lubed. That's about $150-200 worth of bullets (at retail) for about $70. I think I have about $300 of gear (pot, burner, ladle, mold, lube/sizer, safety mask), so that fixed cost is recovered very quickly.
I'm just at the point now where I think I know what the major factors in poor quality are for me, and it's really attention to detail (keeping the mold clean), paying more attention to casting rate in order to manage mold temperature, and sticking with one alloy that behaves predictably. With those things in place, quality is all I need it to be for my kind of shooting--where speed and reliability far outstrip any other criteria, including accuracy. However, I can say with absolute certainty my cast bullets have no negative impact on my shooting accuracy.
Now, if your kind of shooting is more like long range bench rest precision or something, where you might light one up every few minutes, shoot 50 shots and go home until next month--that may be different. Your goal may not be to have several thousand bullets on hand for 500 round practice sessions. In that case, spending $0.10 a bullet (or upwards to a dollar or more per bullet) may not be a factor, and the only advantage of rolling your own might be purely pride and joy or getting out of the house.