I guess we both agree that eating less and exercising more is a good strategy to lose weight

It can be -- for some people. It's probably not a good strategy for other people. The simplest way to find out is to try.

the proportions of the food consumed and exercise necessary to lose weight may be quite different?

Yes, very much so. That's why it says "eat less" and not "eat 1000 calories/day".

And we disagree... about how frequent are these health-related reasons in population, and how often the people with the health-related reasons are given this advice anyway...?

I don't know -- neither of us made explicit claims about that :-) Generally speaking, humans are well-adapted to periods of starvation and fasting can help with some health problems. Diabetes is probably the most widespread disease which will present problems with "eat less" approach.