The user can already choose. If you want it permanent, post it on chain.
If you want it temporary, post it literally anywhere else on the internet.
I guess condensers could adopt a second (casual) layer, which doesn't post to the chain at all; similar to the dissenter browser extension.
I would support the adoption of a mechanism to remove images, binary, ASCII or otherwise, under specific circumstances; but only at the witness level, not by users.