Does Astral Projection spell fail if cast while on the Elemental Planes or Material Echo Planes (Shadowfell, Feywild)?

Further to the question: Can there be portals in the Astral Plane that lead to the Elemental Planes , I wanted to ask does Astral Projection spell fail if cast while on the Elemental Planes or Material Echo Planes (Shadowfell, Feywild)?

According to the Etherealness spell (PHB p238) :

This spell has no effect if you cast it while you are on the Ethereal Plane or a plane that doesn’t border it, such as one of the Outer Planes.

According to the Astral Projection spell (PHB 215):

You and up to eight willing creatures within range project your astral bodies into the Astral Plane (the spell fails and casting is wasted if you are already on that plane).

And later in the same spell description:

Your astral form can freely travel through the Astral Plane and can pass through portals there to any other plane.

However, according to DMG in the description of relevant planar travel spells (DMG pg 46) it indicates the following :

And the astral projection spell lets adventurers project themselves into the Astral Plane and from there travel to the Outer Planes.

Accordingly, for both RAW and RAI, does Astral Projection spell fail if cast while on the Elemental Planes or Material Echo Planes (Shadowfell, Feywild)?