This is verging on an opinion-based question, but I think it is on-topic, since it helps to clarify the syntax and structure of ggplot calls.
In a sense you have already answered the question yourself:
it does not seem to be documented anywhere in the ggplot2 help
This, and the near absence of examples in online tutorials, blogs and SO answers is a good enough reason not to use aes this way (or at least not to teach people to use it this way). It could lead to confusion and frustration on the part of new users.
This fits a lot better into the logic of adding up layers
This is sort of true, but could be a bit misleading. What it actually does is to specify the default aesthetic mapping, that subsequent layers will inherit from the ggplot object itself. It should be considered a core part of the base plot, along with the default data object, and therefore "belongs" in the initial ggplot call, rather than something that is being added or layered on to the plot. If you create a default ggplot object without data and mapping, the slots are still there, but contain waivers rather than being NULL :
p <- ggplot()
p$mapping
#> Aesthetic mapping:
#> <empty>
p$data
#> list()
#> attr(,"class")
#> [1] "waiver"
Note that unlike the scales and co-ordinate objects, for which you might argue that the same is also true, there can be no defaults for data and aesthetic mappings.
Does this mean you should never use this syntax? No, but it should be considered an advanced trick for folks who are well versed in ggplot. The most frequent use case I find for it is in changing the mapping of ggplots that are created in extension packages, such as ggsurvplot or ggraph, where the plotting functions use wrappers around ggplot. It can also be used to quickly create multiple plots with the same themes and colour scales:
p <- ggplot(iris, aes(Sepal.Width, Sepal.Length)) +
geom_point(aes(color = Species)) +
theme_light()
library(patchwork)
p + (p + aes(Petal.Width, Petal.Length))

So the bottom line is that you can use this if you want, but best avoid teaching it to beginners