it seems like besides bouyancy, only cave diving can make you a good cave diver. not many times when you have no vis, and small spaces to dive in.
Until you get to cave level, small spaces are not even in the mix. Most popular caves are pretty large with great visibility, when not blown out by foloded rivers. Some systems are not affected at all by rivers and are generally pretty clear. No vis, is done by closing your eyes during training. Depending on what type of cave diving you do, and where you do it, you can dive places where you may never see zero vis without causing it yourself.
Having said this, Cavern will teach you much of the new skills that will prepare you for your move into the overhead. Cavern is a great course to make a diver much better. You can practice all of your skills anywhere. You don't need an overhead to dive with the proper form that you will learn in cavern. Body position, frog kick, or modifications of the frog lick, managing your gas supply, reel work, getting your equipment where you want it can be practiced anywhere.
When you have become comfortable with cavern stuff, and if you decide to move on, then you do so. A good instructor will not pass you until you have successfully completed the course. The course requires "minimum standards". It is up to you to take those skills and hone them until they are not only second nature, but in excellent form consistently. Many divers stop practicing after a bit. They think "good enough". This is not the instructors fault, it is the diver's for not making these new skill second nature.
If you do cavern and practice this until it is second nature, you will be a much better diver, even if this oil scare clears and you never go further into the cave education. Cavern is probably the best course for any diver to get their diving into proper form.
Good luck if that is what you choose to do. Also let me throw Shirley Kasser into the instructor loop. She lives in Lake Mary. She is cavern and cave 1.
sskasser@hotmail.com Her website is shediver.com