`Render callbacks` is referred as `render prop` in the react community. I also like prop because it's relatively more accurate?

Overall i think we need better categorization about your article which is very interesting to read.

a) can we not change the children component? Yes we can do with the first two approaches, nice!!

b) can we change the children component? Yes we can do with the other approaches, but if I can change the children, what's the point of doing it? Just add a prop then.

I think the approach mentioned here are very useful, but i don't think it should be used for the purpose you mentioned. That's my two cents.