Self-insuring or not having any insurance at all can be done in some areas legally and is done quite a bit. Personally I would not want any student flying my airplane without me on board, because that is the time of highest financial risk if they crash or have an incident, but it can be done successfully and often is. Having the student supply the airplane is a far more financially sound. Many middle aged adults have the means and desire to do this. The drawbacks are that to teach in it you really need to know its intricacies especially if it is not a common trainer, and someone who buys an airplane may also be using that as a way to get around their personal incompetence and I have seen this first hand. At the very least, they may be be inclined to swap CFIs whenever the going gets tough rather than stick it out with one that insists on adequate performance.