Why would a company ever impose binding restrictions on itself?

Hypothetically, or in the specific case of facebook?

Companies imposing binding restrictions on themselves is vital to loads of types of business. An insurance company binds themselves to pay out if you make a valid claim, for example.

To convince customers that they're not just trying to trick them?

It's a PR move. Probably proposed by one of many third party agencies that Sandberg 'wasn't aware of but takes full responsibility for'.

I think it's more likely this is to avoid problems with the slew of dating apps that depend on Facebook now that they're starting to roll out their dating feature.

When they’ve already burned their reputation and need to convince portential partners that they won’t do it again.

I can’t think of any real world examples, though. So this is all hypothetical.

Well basically every company releasing code under an open source or free software license does so it is quite common. I guess the answer to the "why?" is the same as always: they believe doing so is more valuable than not doing so.

To ward off government regulation.