That's already the world we're in except for the fact that small competitors can't integrate with them, or reimplement clients even if they want to. Netflix runs fine on every platform of the large players. I can log into everything with Google, Facebook and vice-versa, the very largest companies often already adjust their infrastructure to be mutually compatible to significant degrees.
It's really only third party incumbents who get locked out regularly, if you're already an Apple or Microsoft you can at least partially get your way with the other big sharks. It's the Signals and IRCs and (until recently) Linuxes of this world who have to exist at the margins.
I also think it's important to point out that nobody has to fully reimplement a services API. If you're one guy, and you want to make a sleek, minimialist facebook client, why not? If people prefer full featured Facebook they can go to Facebook, but at least then there is choice. I wasn't saying either that a company can't have huge market share in this system, just that they ought to do it on the merit of their software, facing full competition. Large companies that provide feature-rich experiences will still win customers who desire these features, so I don't see the downside to my proposal.