That assumes that the narrative point of the pink letter is to create uncertainty. I would disagree with that – the narrative point of the pink letter is to be the catalyst for Jon’s death, the uncertainty is all meta-narrative.
Moreover, the importance of said uncertainty is highly contingent on the letter coming at the end of the book – thus setting up a cliffhanger mystery – which wouldn’t be the case if the book ended with the Battles of Ice and Fire. Instead, the letter would function at a meta-narrative level as setup for the payoff of the battle.