The feywild existed in 3e as an optional plane of Faerie, though 4e put it front and center in its cosmology and expanded it quite a bit (similar in many ways to Pathfinder's faerie plane of the First World). I wouldn't mind a plane of Faerie/feywild in 5e, but it would need to be more careful to forge its own identity based on real world fey myths while simultaneously allowing for the fey-inspired celestial eladrin from 2e and 3e to retain their own presence in Arborea as an outer plane distinct from a more material, less metaphysical fey plane.
I've been wondering about this too. I'm writing a Planescape adventure that features the Queen of Air & Darkness & courts of the fey as one of the thematic elements... How to reconcile Eladrin, their traditional 2e placement in Arborea, and their 4e placement in Faerie?
Definitely agree with you about looking to real world fey myths for the Faerie/Feywild. IIRC fey were often superstitiously connected to the spirits of the dead... or sometimes not explained at all! So there's the more organized view of "an elder amoral nature race living in hiding from humankind" and then there's the mysterious view. I think if the mysterious view was played up it might work better thematically.
For example, why can the eladrin travel so easily to the Prime worlds? Maybe it's because they use the Feywild, which somehow links to Arborea the realm of the elven Seldarine? Eladrin might become the equivalent of the Seelie Court who are made a choice to have morality and to support mortal's free will, thus aligning themselves with the elven gods. So the Court of Stars is comprised of the small number of fey (eladrin) who choose good morals and to serve as muses to humankind. Is their original home plane Faerie/Feywild? Probably, but it's hard to say for sure. For magical purposes they are natives of both Arborea...or possibly both Arborea and the Feywild as suits the whimsical beings.
This opens up design space for what the Unseelie Court would look like? In PS they were linked to Pandemonium, which implies predatory selfishness & madness, the abandonment of meaning, I imagine them as something like the True Fey from Changeling: the Lost...alien beings consumed with sating their own maniacal whims. They've also adopted a moral stance: mortals are chattel and entertainment that deserve to be enslaved. Perhaps once they were natives of Faerie/Feywild, but now they're just as much a part of Pandemonium...or perhaps the Plane of Nightmares...or even Shadow/Ravenloft...it's hard to say with such shifty beings.
Most fey, however, take no such moral stance and are neutral/unaligned in that they have their own magical codes which defy mortal ethics. You could even go the "they were once an abundant prosperous race that was forced into the shadows of the wild lands by human expansion/conquest", so they enjoy mischief to get back at humans. These fey properly belong in Faerie/Feywild.
I guess what I'm getting at is the fey defy sys-admin organizational thinking; their origins are multiple. The most important part are their stories, and these are unique to groups of fey or to individual fey. Precisely placing fey in the cosmology is less important than giving them compelling stories that can hook adventurers into their convoluted politics and flights of fantasy.