I don't see the problem, Neil (you probably know my opinion about these things anyway

).
It is not a minefield to enforce payment for cancelled lessons - what you describe are things that are clearly covered by discretion. I hardly know people who would insist on payment in a case like bereavement, hospitalisation etc, and most people I know who have contracts have a clear paragraph or sentence stating 'teacher's discretion' of some sort.
But yes, I do insist on payment in cases of minor illnesses like colds, because they have been used as an excuse in the past, and I am not taking that anymore. It has to be clear that both sides have certain commitments, and also that I have to make a living of my teaching. Next to nobody credits appointments/lessons/courses missed because of illness - only privat teachers seem to do so, and I really don't get it. We are running a business, not a charity. As much as I feel sorry for people who have colds, but if I do this on a constant basis, I cannot live during winter.
Strictly speaking, it is really not a difference if they sign, or you just hand out terms they accept - and by taking lessons with you, they do, it is then a mutual agreement which is not less binding.
HOWEVER, I found it much harder to enforce, and I got tired of the permanent discussions about whether payment is necessary or not. Not all my students are on contracts btw, but even the ones who take adhoc lessons sign a wee paragraph at the bottom of their registration sheet (adress etc) that they are aware of the fact that lessons missed with less than 48hrs notice have to be paid for, and that exemptions from this rule lie within the
teacher's discretion (not theirs!).
It always sounds like a contract is something that is frightening or God knows what. I really don't get this. Call it 'agreement' or 'terms and conditions' if you are so scared of the word, but it really doesn't make a difference. Just by not letting people sign, it's not any less valid. The only difference is that something that isn't signed is easier to dodge. I wouldn't get any help from the MU for instance if I don't have it writing.
Teachers with contracts are certainly not any less sympathetic towards peoples' problems, far from it.