Sure, but that's not what the saying literally says. It says "only a poor craftsman blames his tools". It makes no mention of the tools being actually fit for the purpose. They should have specified that.

And even if it is the "right" tool (a hammer for a nail), what if the hammer is a plastic kid's toy?

I think this saying makes far too many implicit assumptions about the type and quality of the craftsman's tools.

It's just to me this seems like taking issue with 'the proof of the pudding is in the eating' because sometimes what I'm eating isn't pudding, and some people don't like pudding at all. All sayings have some implicit context or scenario in which they're applicable.

I suppose so, but for some reason that particular saying rubs me the wrong way. With 'the proof is in the pudding', I can get the meaning, and you could substitute any food. It just means (if I understand correctly) that if someone makes good pudding, you can tell it by eating the pudding. Even if someone doesn't like pudding, they know some pudding is better than others, or can substitute some other food-of-choice here for the same meaning. I don't think the craftsman-tools saying works the same way. For instance, it leaves me with questions like: are the tools actually selected by the craftsman, or were they forced on him by someone else? The pudding saying just doesn't have all these complications as far as I can see.