Look at the 5e cosmology map:
Astral Plane → Elemental Chaos → Ethereal Plane → Material Plane
The Astral thought emanates the Elemental Chaos, out of which the forms of Elements take shape, gaining ethereal force, to become matter.
There is a "Crossing" between the Neutral planes and the Elemental Chaos. Similarly, there is a Crossing between the Good planes and the Feywild, and a Crossing between the Evil planes and the Shadowfell.
The Genasi are in the place of this threshold between Astral thought and Elemental form.
I've seen the 5e cosmology map. It's a diagram representing a conceptual framework, not a literal physical map you can use to navigate walking from one plane to another.
These supposed "crossings" from the Upper Planes to the Feywild and the Lower Planes to the Shadowfell pass through the Elemental Chaos, which completely surrounds the Inner Planes and separates them from the Outer Planes (according to this diagram), so should we just replace tieflings and aasimar with genasi now too? By your argument, they should all be descended from elementals too...
More to the point, those "crossings" are the "borders" between the various elemental planes, which the chart of the Inner Planes in the DMG shows to be very much filled in with what I would describe as the para-elemental planes, where two of the big four elemental planes overlap with one another. That "crossing" linking the Upper Planes to the Feywild is the Frostfell (Para-Elemental Plane of Ice).
Also, if the Feywild and Shadowfell are connected to anything, it's the Positive and Negative Planes, respectively, which are shown on another diagram as domes encasing the Great Wheel from above and below. Not the Outer Planes.
Just because two things are drawn next to one another on a "map" doesn't mean it's actually possible to travel from one to the other - the map is not the territory. This chart was designed to show new players the major planes that exist and their overall groupings (i.e. Outer Planes, Inner Planes, and Material/Echo trio). I would hardly call its arrangement definitive.
Historically, the Inner Planes have been contained within the Ethereal and the Outer Planes within the Astral, with the Material Plane being where the two meet - a giant, cosmological Venn diagram. I do not consider that to have changed.