It would be great to have an mobile version of magic wormhole, though sadly I'm not an app developer so while I would really like to implement it, it's outside of my skillset.
https://play.google.com/store/apps/details?id=io.sanford.wor...
https://github.com/psanford/wormhole-william-mobile
One disadvantage is that current magic wormhole doesn't support resume but they plan to implement it.
Another app that you might have heard of is croc, but it doesn't seem to be secure:
This means that all solutions will either require sender and receiver being connected to the same wi-fi network (possibly provided by one of the devices involved, which is pretty awkward and also has its downsides like unintentionally sharing the internet connection [2]), or resorting to Bluetooth LE (resulting in extremely slow connection speeds not really suitable for file transfer).
Finally, any solution requiring installing a third-party app has an inherent growth impediment given that sharing the app itself is all but impossible when offline.
[1] Wi-Fi Direct would seem to be ideal for this use case but is Android only, and even there does not seem to reliably work on all devices. Even Google's native AirDrop alternative resorts to using mobile data in some circumstances/device combinations.
[2] It seems possible to avoid this given that the Android device is providing the network: https://developer.android.com/reference/android/net/wifi/Wif...
The Wi-Fi Alliance have been trying to standardise something not dissimilar to AWDL under the name “Wi-Fi Aware” (NAN/Neighbour Awareness Networking), but it is not widely implemented and will probably never be supported by Apple either, limiting cross-platform potential.
There is both a webapp (which works on mobile browsers) and a command line client. The command line client can even display ASCII QR codes for easy access on mobile devices.
The only problem is long-running background uploads/downloads, but I don't think a mobile app could help there (at least on iOS).