I usually have beginners flying their trainers inverted long before they learn to land. I teach them basic acrobatics early on for two reasons:

1.) - that is why most of them want to learn to fly in the first place.

2.) - It is more stressful than flying around in circles, teaches them what to do in unusual attitudes, and makes them more relaxed when they start doing approaches to the runway.

Now if your trainer has ailerons, flying inverted is only slightly more difficult than flying upright. If it has rudder and elevator only, it becomes slightly more interesting, but still not difficult with a couple of minutes of instruction.

The goal (mine at least) is to turn out a pilot that can fly anything. I don't consider the job finished just because they have solo'ed and can take-off and land. I have spent years working with different pilots, as they upgrade their models, their skills and techniques. It is rather pathetic how few pilots reach their full potential, I know that I haven't. Often, they are too proud or too embarrassed to admit that they need more instruction, and quite frankly too often the available instructors do not have the skills or knowledge either. In that case the only option may be to read more and experiment at the field to put theory into practice.

Another problem is that there are often too many students and too few instructors. You do not have to be the greatest pilot to help with instruction. Assisting with basic field procedure, radio, engine, tank setup, and just talking to new students is an enormous help to a harried instructor.

I am not sure how standing on a beach ball in a pool of water is relevant, nor the pretty pictures of plates pulled through water. But whatever.