> •  The curved sides of the projection suggest the spherical form of Earth.
    > •  Straight parallels that make it easier to compare how far north or south places are from the equator.

So why pick this over, say, Eckert IV or something from the Tobler Hyperelliptical family?

There is perhaps an additional argument (present on the wiki page [1], and elaborated on the paper introducing the projection [2]) that the equal earth projection is computationally easier to translate between lat/long and map coordinates, as it explicitly uses a polynomial equation instead of strict elliptical arcs. (This is the main argument presented against Eckert IV.)

The paper also lists some additional aesthetic goals: poles do not converge to points (ruling out Tobler Hyperelliptical), and meridians do not bulge excessively.

In fact, the paper describes Equal Area to be a blend of Craster parabolic and Eckert IV (then aesthetically tuned to avoid being stretched too much in either direction). It is also notable that the Equal Area paper measures both lower scale distortion and angular deformation for Eckert IV.

[0] https://en.wikipedia.org/wiki/List_of_map_projections#pseudo...

[1] https://en.wikipedia.org/wiki/Equal_Earth_projection

[2] https://scholar.google.com/scholar?q=doi.org%2F10.1080%2F136...

edit: I found https://map-projections.net/singleview.php which you can view a bunch of other possible candidates by selecting Pseudocylindric + Equal-Area.