I should probably preface this with that I haven't actually had a chance to play the game yet. I'm just looking at the materials and trying to learn for now. Not to mention, it doesn't really impact my character-designing decisions too much, but the more I think about it the more odd it is.
It being a background instead of a heritage notwithstanding, the only reason I could think of for it not making you undead(or at least having the option) was balance concerns regarding an undead player character. I mean, obviously, right? But...then I remember you can just literally play as a skeleton.
So...what's up with that? Am I the weird one here?
It might be due to creatures with the undead trait die immediately at 0 HP (not to dying 1 condition). So they might have wanted a similar vibe to actual creature revenants but without removing player character survivability.
Also the actual undead heritage you are referring to gets Basic Undead Benefits which notably stops them from dying at 0hp immediately, but also gives immunity to death effects and better vision, undead hunger etc. On the other end, an Undead heritage cannot have stabilize cast on them but a revenant can, undead are destroyed if they die so cannot be brought back to life again, whereas the Revenant can keep being brought back to life and become Revenant2 I guess.
So the Revenant background gives some aspects of the undead without giving all the full blown benefits of an entire heritage option and not as many drawback either. I'm seeing it now as Revenant == Undead-lite.
Hm. How much of a nerf would it actually be? Not really all that sure, and I suppose if Undead are so much weaker for some reason it would make sense(still silly and weird though, like you said).
But then why not, as briefly mentioned in the post, just make it a heritage instead? It would make more sense in general anyway. As I was looking I also saw at LEAST two other "back-from-the-dead" backgrounds, so there wouldn't even really be anything lost.