Quote - By "ineffectual", do you just mean it will give a zero result? Or do you mean that using a math node zero plugged into the value channel will cause the internal node calculations to be skipped; whereas simply setting the value to zero, or the colour to black, will not?

I'll give you my understanding. Then Bill can give you the real reason.

My understanding is that plugging in a maths node that does nothing tells that channel to send no information to the renderer.
That channel still has information that it sends to 'preview-mode' so it will continue displaying whatever colour is in that channel or whatever colourMap may be attached to it.

Can't for the life of me sort out how BB figures these things out. No wonder he's so focused on maths as a solution: it IS!
Consider 0 + 0 = 0. This does nothing.
Well, to my mind it does something - it is adding, which to me is an activity, but you could also see it as "put +0 together with +0 and what do you get?
And then there's the whole equation operator.
Now, to my knowledge there's no such thing as plus or minus 0... zero is zero

Anyway, adding zero to itself is achieving nothing.

You can see why I suck at maths: I over-analyse it! So, the activity of "do nothing" might be telling that channel to "send nothing".

K, I give up. Next witness...

Monterey/Mint21.x/Win10 - Blender3.x - PP11.3(cm) - Musescore3.6.2

Wir sind gewohnt, daß die Menschen verhöhnen was sie nicht verstehen
[it is clear that humans have contempt for that which they do not understand] 

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