In South Africa Twitter is huge. In Germany, Facebook is. Instagram is big in the UK. Now take the possibly not unusual scenario in which a South African lives in London and has family in Germany.
Granpappy in Berlin would search for his grandson in London from Facebook but finds him on Instagram. He'd add the grandson as a friend and see the grandson's Instagram photos in his Facebook feed.
The South African guy in London searches Instagram for his nephew in South Africa, and finds him on Twitter. And sees that Twitter account's posts in Instagram.
If someone on Facebook finds me on Instagram, Instagram could notify me that Mr. X is searching for a profile that matches mine, and ask if I want to allow access to my stuff. If I decline he can't. Federation, with user control and consent.
I think it could work. And even if it was useful to a tiny monitory at least there's real choice. Inclusive of all.
I can see how it should be easy to send content from foo#twitter.com to bar#facebook.com as individual messages, format issues not withstanding, if foo and bar have agreed to correspond. But which end would manage the existence of that relationship and push/pull the data?
Maybe it needs third-party brokers to do it?
Interestingly I can see some parallels here with the current status of banking in the UK. After centuries of operation as "closed systems" there are now rules to force banks to provide APIs so that new entrants can offer inter-operation services. Maybe in a hundred years social-media companies will be forced to do the same? ;-)
Also, such federation, if not open to third parties (easy to justify with spam, malicious parties, etc) can actually strengthen the current big platforms against competition.