There is literally a huge and prominent link entitled "Equal Earth Projection" in the middle, at the top, that when clicked take you to a description of what the intent of the projection was:

    It was created to provide a visually pleasing alternative to the Gall-Peters projection, which some schools and socially concerned groups have adopted out of concern for fairness. Their priority is to show developing countries in the tropics and developed countries in the north with correctly proportioned sizes.

    In addition to being rigorously equal-area throughout, other Equal Earth projection features include:

    •  An overall shape similar to that of the Robinson projection. (The Robinson, although popular and pleasing to the eye, is not equal-area as is the Equal Earth projection).

    •  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.

    > •  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.

Yes, and there are also already multiple equal-area projections with similar properties, too. For example, the Goode homolosine "orange-peel" projection only loses out by failing to show contiguous oceans (emphasizing land masses instead) and having a discontinuity where two simpler projections are joined. It gives equal-area projection and improved shapes (as compared to fully homolographic projections) while still showing "curved sides [that] suggest the spherical form of Earth" (arguably, far more so). Its parallels are straight, and furthermore they are equidistant in the central latitudes (in which it's based on a sinusoidal projection).

Oh, and it was developed over a century ago, and already in common use when Arno Peters started his activism for the Gall-Peters projection (called this even though Peters made no refinements in independently developing a projection identical to Gall's 1855 work, and even initially mis-described it).