The problem with your suggestion is that your partner might send a different but equally "guaranteed success" strategy (e.g. "...opposite color of the mixing result"). Then how do you agree on which strategy to use?
Or, take the critique mentioned in the article: Is red + blue called violet or purple? Same problem: You would need to agree on one name, and this conflict is not solved by you sending what you would call it - your partner might do exactly the same but with a different name.
I see where you're coming from, but for the problem to be solvable at all we need to presuppose some base level of agreement about the world between you and your partner. To take your critique even further (I haven't seen the article, original sub was a twitter link) how do I know that my partner agrees with me on the set of primary colors?
Ultimately the problem is constructed to prompt a discussion so any reasonable "solution" would do, or if the stakes were life and death maybe the rational solution is to play forever as suggested by other commenters.
Or, take the critique mentioned in the article: Is red + blue called violet or purple? Same problem: You would need to agree on one name, and this conflict is not solved by you sending what you would call it - your partner might do exactly the same but with a different name.