This is closely aligned with the GDPR's "Right to be forgotten", yes this is in relation to different information but I'm simply describing its intent. But eventually, this level of control should be given to all of us who share content on the internet. That we the curators of such content can ask of the provider to take reasonable steps to remove such content. And that if a provider wishes to restrict how widely dispersed its creators content travels then that's fine. Just because something has been posted online, doesn't mean it needs to travel far and wide.
Now yes, if I post something on the internet and I never touch it again I'm happy for it to hit the Wayback machine. However, I believe it to be important that if I did ever want that information I created to be removed, I'd have the ability to do so. Now if the Wayback machine does not allow this replication, then I understand why Quora do not allow them to use it.
If anything its a battle on both sides, a battle to provide control to the content creators around the content they create. And a battle with trying to archive everything that exists on the internet and making it publicly available regardless of the content creators current wishes.
Don't get me wrong, if you post something online expect it to be on the largest most accessible encyclopedia of information of all time. But times are changing, and we are starting to implement controls to protect our digital identity and the information we create online. My argument, is that if a content provider wishes to restrict how far and wide the information I curate on its service is spread, then there's nothing wrong with that. We should not be shaming content providers who wish to provide as much power to the curator as possible.