Agency (as you define it: being able to control your data in the way that you want to) is in direct conflict with another key goal of user experiences:
With social media it is historical integrity. Another goal that can be thwarted by "more agency" is operational integrity.
Historical Integrity — This is Facebook, Twitter, even StackOverflow. @Yuriy addresses this with a great simple example. In addition, look at our own StackExchange software. You can edit your comments, right? Wrong. All you really have is an **oh-sh**** button. You have 5 minutes to rethink and reword what you typed in your comment, if you hit [Add Comment] too hastily, but then your comment is locked into history forever, (and marked as modified)...
But you can delete it, and repost right? The important thing about this is that the new comment gets put after the rest of the conversation so that you can't hijack history out from under other participants.
Operational Integrity — Look at iOS. One of the key tenets of iOS is a very tightly controlled system. This gives more control for Apple to give higher guarantees for many aspects of the experience: Battery life, crashing, viruses, malware (App Store approval process), etc.
Some users don't want this. They go with Android. But this is one reason why task managers and advanced cache managers end up being popular on Android. It's a trade-off.
@twhitlock is correct that cache invalidation does introduce technical challenges.
But look at all the stuff Facebook does let you edit (every little bit of your profile, photo captions, tags, album captions, album arrangements, notes, events, friend lists, fine-control security settings, etc.) Facebook can handle the editing. They don't let you because it's a core part of their designed and controlled experience.