I don't see why "role and use" would be an adequate substitute either.

I'll again refer you to the Sequences. I think Eliezer did an excellent job explaining why definitions are so inadequate and why role and use are the adequate substitutes.

As I mentioned, meaning critically depends on the subject and the context. Sometimes the meaning of the p-value boils down to "We can publish that". Or maybe "There doesn't seem to be anything here worth investigating further".

And if these experts, who (unusually) are entirely familiar with the brute definition and don't misinterpret it as something it is not, cannot explain any use of p-values without resorting to shockingly crude and unacceptable contextual explanations like 'we need this numerology to get published', then it's time to consider whether p-values should be used at all for any purpose - much less their current use as the arbiters of scientific truth.

Which is much the point of that quote, and of all the citations I have so exhaustively compiled in this post.