The reason we fight against censorship (which is what this debate comes down to) with literal religious fervor is because that's how the other side fights for it.
Don't want it archived forever? Don't put it on the Internet. Seems simple enough.
If Archive.org had your attitude, I would actively oppose it. Removing private, personal info is not censorship. And nothing about "just don't put it on the Internet" is simple. What if someone hacked your devices and then put it on the Internet for lolz? What if you shared it in confidence with someone you trusted, who is intentionally putting it on the Internet to hurt you? What if you accidentally pasted the wrong thing or uploaded the wrong file? What if you were a child and didn't understand the dangers?
There obviously should be ways to ameliorate your mistake, which is why it is absolutely critical that Archive.org has a removal process.
Don't want it archived forever? Don't put it on the Internet. Seems simple enough.