One thing to check in canon would be the scene where the Wizarding minister pops in to the British PM and gives him a status report. I can't remember whether it is implied that PMs are routinely obliviated after their terms are up.
From the flashback scene near the beginning of Book 6 Chapter 1, where the Muggle PM first meets Cornelius Fudge:
“But then,” bleated the Prime Minister, “why hasn't a former Prime Minister warned me — ?”
At this, Fudge had actually laughed.
“My dear Prime Minister, are you ever going to tell anybody?”
So it's implied that no Obliviation is needed. On the other hand, I wouldn't it past Eliezer to decide that this is not credible in a story for adults. And after all, Fudge never really answered the question.
ETA: There is now a third thread, so send new comments there.
Since the first thread has exceeded 500 comments, it seems time for a new one, with Eliezer's just-posted Chapter 33 & 34 to kick things off.
From previous post: