For the patient I think the decision actually is binary - either (i) I contact a doctor about this skin lesion now or (ii) I wait for a bit to see what happens or do nothing. In reality most skin cancers are very obvious even to a non-expert and the reason they are missed are that patients are not checking their skin or have no idea what to look for.
I think you are right about the incidence - would be better to be a more balanced distribution of benign versus malignant, but I don't think it would be good to just show 99% harmless moles and 1% cancers (which is probably the accurate representation of skin lesions in primary care) since it would take too long for patients to learn the appearance of skin cancer.
I am a skin cancer doctor in Queensland and all I do is find and remove skin cancers (find between 10 and 30 every day). In my experience the vast majority of cancers I find are not obvious to other doctors (not even seen by them), let alone obvious to the patient. Most of what I find are BCCs, which are usually very subtle when they are small. Even when I point them out to the patient they still can't see them.
Also, almost all melanomas I find were not noticed by the patient and they're usually a little surprised about the one I point to.
In my experience the only skin cancers routinely noticed by patients are SCCs and Merkel cell carcinomas.
With respect, if "most skin cancers are very obvious even to a non-expert" I suggest the experts are missing them and letting them get larger than necessary.
I realise things will be different in other parts of the world and my location allows a lot more practice than most doctors would get.
Update: I like the quiz. Nice work! In case anyone is wondering, I only got 27/30. Distinguishing between naevus and melanoma without a dermatoscope on it is sometimes impossible. Get your skin checked.
I have quite a few patients from the UK who have had several skin cancers. Invariably they went on holidays to Italy or Spain as a child and soaked up the sun.
Keep up the great work.