I wouldn't say it's the same thing, necessarily. Reincarnation, depending on the faith and whatnot, typically has the soul remain as it was when it was sent through the process of reincarnation. In such a scenario, things like dreams or story ideas or Deja Vu could actually be them remembering some bits and pieces of their past lives. Erasure, however, is different. Sure, we came from "nothing," but that doesn't really help sell the idea.
As an example, let's say someone makes a sculpture from clay, destroys it before it has a chance to be turned solid in a kiln, and throws it back into the pile of clay. If they make the sculpture again they aren't actually remaking the old sculpture, no matter how exact they sculpt it. The old sculpture is already long gone, completely erased. They are simply making a new one that happens to look like it. That's nothingness. You don't reincarnate, you are literally dissolved and then the energy or aether or whatever is recycled. At least with reincarnation there is a chance you can remember your old lives, or barring that you at least still continue to exist between lives even if you don't remember them.
Personally I'd much rather reincarnate and remember my lives, so erasure is something I would want to avoid at all costs. To be reduced to nothingness and recycled is to lose my sense of self and my existence, and I don't know anyone (far as I'm aware) who would actually want that.
Edit: With that said, if someone does want erasure then that's their own choice. Just as those who no longer wish to live make the choice to end their lives, I'm sure there are those who no longer want to exist, to think, and would thus choose oblivion over continued existence. Just so long as they don't drag anyone else into their desire for "peace" if no one else wants it.