It's just a hot-button of mine
I think of the p-value as a point of intersection between statistics and ethics. As you know, a 95% confidence interval is by far the most commonly used, but it's still somewhat arbitrary. Whenever I do hypothesis testing (which, granted, isn't all that often anymore), I explore different intervals if only to glimpse the "lay of the land" (which might not need quotes if you're dealing with geostatistics!)
Anywho, I've long thought that an explanation of why a certain p-value was chosen, and how the hypothesis faired with different values, would be a simple and transparent way to help explain one's determinations.
Just an non-specialist's opinion.