"Fiendlish elf" is actually a thing in the lore and it's called Fey'ri. Those are sun elves with demon blood specifically. There's also wisplings (halfling/demon), tanarruk (orc/demon) and maeluth (dwarf/devil). And some other assorted fiendish bloodlines.
As cool as it could be, I don't think it would work well in 5e-based game. 3.5, I believe, had half-whatever templates, but it's no longer present in 5e. There's also a matter of occurence - tieflings are rather common, but the others are not (afaik) and imo should be reserved for NPCs.
Fully agree on more customization though. It's already great for tieflings, but could be even better!