Microsoft aggressively deployed it in the 1990s with the US Government. It didn't work at all ultimately. Nobody outside of Microsoft's management bought into the premise (they either didn't actually buy into it either, or they were wildly delusional, hard to tell which it really was). Once the DOJ took the Microsoft case seriously, they cut through Microsoft's fluff like a buzzsaw.
It doesn't work very well at all with a determined government, which will zero in on specific market abuses (rather than getting caught up in bullshit PR fluff). Primarily it's one part PR play with the public brand & image, and one part time delay. Facebook would love nothing more than to have an opportunity to burn years of time by being given a chance to argue round and round about all the competition they face.
Microsoft laughably couldn't stop repeating how they were fighting for their right to innovate (which eg had next to nothing to do with their serious OEM abuses). Every other word out of Gates and Ballmer's mouths for years was a variation of innovation. They beat that drum to death, it made no difference. They tried playing the widen the competition pool card over and over again, that also made zero difference.
No serious regulator will ever believe the competition everywhere premise. I generally don't believe it's aimed at actually convincing a serious regulator, either. The sharks that work for giants like Facebook know it's not an actual strong legal argument, which is why I believe it's one part stall tactic and one part public image support. There's a small chance it could cause some skepticism among less determined regulators as a fluke benefit.