Deriving from prog-mode or from text-mode doesn't mean much in practice.
I see it as less of a formal taxonomy of programming languages, and more
of a convenience measure to make changes that (vaguely speaking) "all
programming modes" or "all text-related modes" have in common. E.g. I
have this in my init.el:
I think this is kind of what it boils down to. There's one discussion to be had about whether YAML is a programming language and one whether yaml-ts-mode inheriting from prog mode just makes it nicer in practice.
I haven't seen anyone argue that YAML is a programming language per se, and I don't believe that either. However, to me there is a prevalent feeling that it would be nice and consistent with the other elpa shipped modes of similar languages inherit from prog mod.
As to me calling yaml-mode inheriting from text-mode arbitrary; I mean that in the sense that it was not discussed. It was done with a reason and as a conscious choice, but it was a singular maintainer's choice in a non-GNU elpa package.
Best,
Romanos