And it's worse than that - if it's a photo of both you and them, there's an immediate impasse. Does their right to take their data trump your right to keep a hold of it? Does it depend on who took the picture, or who uploaded it, or when it was taken or how embarrassing it is?

I'm not saying these aren't answerable questions, but I'm very skeptical that the answer is so obvious and non-controversial that we should legally enforce it against all social media platforms.

Here's where law gets complex. Who took the photo? They hold the copyright. Who's in the photo? They have some [limited?] publicity rights. Perhaps those in the photo would need to consent to have the photo republished, which is not, IMO, technically enforceable, but only legally enforceable when someone hires a lawyer/files suit.

My question is limited to "the list." I.e. this is the list of people to whom I connected on this network and, perhaps, the connection type (e.g. followed them, allowed to follow you, both tagged in some post, etc.)

But to add my thoughts to your question: I have a photo, I uploaded it to my account, it's my 'data' and I've simply shared it with you (or made it public) such that it is displayed to you. That doesn't make it your data, meaning you don't get it in an export dump. Perhaps you have a client that makes copies of published posts from your network, but exporting those things you consumed (which are not yours, to which you do not have a 'license') should not be the intent of this export functionality.