We really need to figure out how to encrypt everything on device with keys controlled by the owner of the device.
..but impossible to have unless you control the operating system that is distributed with phones that normal people will use.
Any recordings should be kept in something akin to password manager.
Heck, all of my data in any app should be kept in something like that.
That being said, I do actually expect that this stuff will (generally*) stay on-device. Apple's oddly good about that.