Bayes factor appear to solve this issue. I disagree that this is a basic education issue. It is a lack of agreement among scientists as to what statistical analysis is appropriate.
There are at least a couple of statistical fallacies in this conclusion. And there isn't a lack of agreement about that.
One problem with p-value tests is precisely that people misunderstand what the p-value means, which is where basic education comes in. It could save people from believing a lot of things they shouldn't. (Like many health and fitness crazes over the last generation, for instance) Or at the very least, we could train science journalists.