Firstly, social media's only incentive is to make your data as widely available as possible (in the interests of ad revenue), and maintain a good relationship with the government in their jurisdiction. Every other existing "privacy" setting on Facebook, LinkedIn, etc is already obfuscated to the point of unusability, for this reason, and "travel mode" would be no different.
Secondly, lets imagine that FB did implement a watertight "travel mode" that hid your embarrassing data effectively while you were travelling. Third parties would just start capturing and storing posts while you have "travel mode" off, and sell that to CBP, or whoever else wants to pay for it.