AEA has I gather gone to a system where you cannot use asterisks. I think that's a mistake-- asterisks developed and are still widely used because there are many good reasons to compress continuous information into categorical bins, full stop.
I often have to go through and circle or mark the effects that are notable, which is just a little easier than putting back in asterisks. It could well be that better visualization would convey information effectively without asterisks (e.g. confidence intervals so one can easily see "distance from null=0", say, and the eye can essentially imagine the strength of effect in NHST which binned p-value is getting at.
From a design point of view, it's usually a bad idea to prohibit one kind of visual shortcut without suggesting or even requiring another.
There's also a recent paper analyzing a journal that *banned inferential statistics* (p-values, F-stats, confidence intervals).
An analysis of papers afterward concludes that
"We found multiple instances of authors overstating conclusions beyond what the data would support if statistical significance had been considered. Readers would be largely unable to recognize this because the necessary information to do so was not readily available."
In other words, asterisks are just an author's way of making salient what they think a casual reader (with a normal brain that processes symbols more rapidly than language) should take away. If you take away the asterisks you get more confusion, more hyperbolic language, or something.