You can have that if you want it. But you don't need it. Just because one PC happens to belong to a certain lineage doesn't mean there has to be others the same on that world. As Rocket Raccoon says: "aint no thing like me, 'cept me."
Also, I don't think Nentir Vale counts as classic, but I'd love a 5e setting guide set there, certainly long before more boring or one-note classics. Best D&D cosmology by far; and I say that as a hard-core Eberron fan.
This is the one setting I love and home brewed to
Death. I dropped the art (love tony”s art but it didn’t fit my homebrew). Basically kept the factions and portals and NPC’s and made it a techno/modern setting spanning the planes. They had technology drawn from all over the planes from a trillion times a trillion worlds in a trillion times a trillion alternative material planes. Sliders also where u could meet yourself from an alternate timeline or parallel universe. And sigil was the center of knowledges and tech and magic for a price. A lost tony stark from earth 8A213z2 ran a mechanic shop fixing broken hover crafts trying to find a doorway home. But that was me and alot of homebrewing.
It just makes sense to me that planescape mechanus and sigil would have a higher level of technology. And I do the nine hells right out of the industrial revolution with the factories and mass production. I am generally very pro industrial revolution. But it’s the nine hells I focus on the worse aspects of it by having sweat shops and things like that. Not everyone was a Ford.