You're consenting by posting it on public internet in the first place.
And requiring an explicit opt-in would basically mean no IA.
To be clear, the IA is a positive, maybe even a great one. But it skirts by because most people don't care. (They did as you say post whatever on the public internet.) Add the facts that they're a non-profit, aren't trying to monetize their hosting, and will generally take things if the owner asks.
Libraries and other archives have some very limited special rights (which mostly relate to making physical backups of physical books). But invoking "library" isn't some general get out of jail free card with respect to copyright.
These rights are also under constant attack: It's normal to charge libraries exorbitant prices for digital materials compared to their analogue counterparts, for example.
It effectively is. Your consent is not required, and people are doing far worse than just keeping it available (Clearview; there are also reports of people hoovering up encrypted data to crack in the coming decades when we're post-quantum).
This is no different than demanding people not keep track of anything else, and attacking archive.org might make you feel better, but that won't make anyone else stop.
1.) Most people won't opt-in because a significant majority accept defaults and don't opt into most things.
2.) For people like yourself probing a bit deeper, you might well ask whether you really want to give up your ability to decide you don't want something you thought was so funny when you wrote it at 20 now that you're a politician running for office or up for a political appointment.
It's fairly unethical.