I'm pretty sure that AT&T and Standard Oil also had branches that did not have a monopoly in their respective areas, but that didn't stop the splitting of the companies.
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.
If you're a monopolist, widen your pool of competition to include anything you possibly can.
If your employees consume fruit at work, proclaim you're competing with Chiquita bananas (and have a tiny share of the fruit market).
If your employees ever fly on planes, proclaim your position in jets is terribly weak next to Boeing and Airbus.
They're not a social network, they're considerably trailing YouTube with Watch. They're not a social network, they're trailing Craigslist with Marketplace. They're not a social network, they're badly trailing Android and iOS in app marketplaces. They're not a social network, they're badly trailing Amazon and Google in smart speakers and home tech. And so on the lie goes.