Hi, MM. I didn't consult any books over this and was relying on memory from decades ago! I considered the distinction between a phrase and a clause to be that a clause contains a finite verb, but I see that you use the concept "non-finite clause". In my view, in "Painting a child is difficult", "painting a child" is a
noun phrase (or non-finite
noun clause in your view), not because it contains a gerund (verb functioning as a noun), but because the entire phrase acts as a noun in the rest of the sentence (subject of "is"). Certainly, though, it would be difficult for a
gerund phrase/non-finite clause (as it is when analysed internally) to have another function.
But just to make my viewpoint clear, consider the sentence, "Why he left is a mystery", "why he left" is a
noun clause; it doesn't
contain anything acting as a noun but, as a whole, it is the subject of "is a mystery".
Maybe this is the beginning of a debate. It's a pity that text-books lump everything together as "-ing forms", an entirely useless term as you can see for yourself that they end with -ing!