>social media feels more like a private conversation in a public space

Then it wasn't very smart of you to post something publicly then.

You should be able to choose what things you want public or private, but if your intention is for public, I don't think you should be able to delete it. You can make amendments to what you say, but you shouldn't be granted the ability to choose what other people remember. Otherwise, private conversations or just saying nothing are alternatives.

>At what point does archiving everything people do constrain their ability to live freely in the present?

The point at which information you intended to post privately is made public without your permission.