Someday we'll probably get an international standard for mobile passports, but it's not happening any time soon.
Until recently I worked for Google, on Android, and participated in the International Standards Organization (ISO) committee that would be tasked with defining the technical standard for mobile passports. To be clear, the ISO committee can't actually issue such a standard, passports are standardized through ICAO. But the relevant ICAO committee delegates the technical work to an ISO committee.
The current situation in those committees is that the companies who make passport booklets and passport acceptance infrastructure are successfully fending off attempts to define a standard to enable mobile passports. They have gotten a new standard (called the "Digital Travel Credential - Physical Component", DTC-PC) approved that allegedly facilitates mobile devices with passports but isn't actually usable. Apple has refused to implement it and Google isn't making any moves to support it (though someone could write an Android app that does; all of the necessary APIs are available).
One of the main sticking points is that the ICAO committee is currently specifying that any digital travel credential should not support data minimization, meaning the ability to present just a subset of the data. More precisely, they specify that data minimization is a non-goal, but since a protocol that supports retrieving and authenticating a subset of the data without leaking any of the un-presented data is always going to be a lot more complex than a protocol that sends the entire data set in a single signed blob, any technical proposal that supports data minimization will be shot down as needlessly complex.
The ICAO's position on data minimization is that the only use of travel credentials is presentation at border checkpoints, and at border checkpoints you always have to present all of the data, so data minimization support is unnecessary. The counterargument from many people is that passports are used in many contexts other than border checkpoints, and many of those other contexts don't need and therefore shouldn't get all of the data in the passport. Since both Google and Apple insist on data minimization as an essential feature, there's not much movement happening.
My guess is that it will take 2-3 years to break the current logjam on even beginning work on a real, usable standard, then another few years to define it and put it into effect, then a few years more for most border checkpoints to accept it, and perhaps a few years beyond that for people to become sufficiently confident in their mobile devices' reliability that they will travel without a paper passport booklet. So... 20 years or so.
The work with the TSA is on derived credentials that are based on your passport (and securely authenticated), using a protocol derived from the ISO 18013-5 mobile driving license standard. It does support data minimization and looks a lot like what an eventual passport protocol should look like (IMNSHO -- note that I designed big chunks of the 18013-5 standard), but will not be accepted at any border checkpoints.