This was the business model of Compuserve. And AOL. And then a little thing called The Internet got popular for a minute in the mid 1990s, and that plan suddenly didn't work out so well for those captains of industry.
But here we go again.
Instagram tries to lock you into their app more than any of the other services. They are hardly even on the Internet at all -- it's more like a service that exists solely on the cellular data networks. Instagram is a dialup BBS. It is the most locked-in and user-hostile of the bunch, as I will now express through the medium of a
|Has an app that lets you post text and images:||✓||✓||✓|
|Has a web site that lets you post text and images:||✓||✓||☓|
|Has a web site that lets you delete or edit your posts:||✓||✓||☓|
|Can send you replies by email:||✓||✓||☓|
|Has an API that lets you post text and images:||✓||✓||☓|
|Has a web site that lets people see your posts:||✓||✓||✓||But only as of 2012!|
|Has RSS feeds:||☓||☓||☓|
|Used to have RSS feeds:||✓||✓||-|
|Real Names policy:*||✓||☓||☓|
|Hates the gays:*||✓||☓||☓|
For these reasons, I've mostly just ignored Instagram over the years -- my attitude was, "Oh, you don't want to be a part of the Internet? Welcome to oblivion." But it seems like these days, as Twitter begins circling the drain, the cool kids are ditching Twitter for Instagram.
The thing that makes the Internet useful is interoperability. These companies hate that. The thing that makes the Internet become more useful is the open source notion that there will always be more smart people who don't work for your company than that do, and some of those people will find ways to expand on your work in ways you never anticipated. These companies hate that, too. They'd rather you have nothing than that you have something they don't own.
Instagram didn't even really have a web site until 2012! You may not remember this, but it didn't used to be possible to see Instagram photos from a web browser at all.
If that doesn't sound insane to you, I can't help with your problem.
Now don't get me wrong, Facebook is by far the worst of the lot. This is largely due to their size and power, but the fact is that they shit on their users far more than the others do. This is a quantitative difference, not qualitative, but it's still extreme. As I've said before, if you work for Facebook, you should quit; it's the only morally defensible thing for you to do.
But wow, Instagram's design decisions are among the most user-hostile and Internet-hating that I've ever seen.