Complete transparency from end to end would require more than just open source. You'd have to be able to build and run the software itself, which on an iPhone costs $99 a year to do and poses significant technical challenges. To go further you'd have to transparency at the hardware level as well. Your own device, built by you, with software you compiled yourself. Maybe then you'd achieve the level of security that you're aiming for, assuming you are competent enough to evaluate the software and hardware you are using.
It wouldn't be for iPhone. For Android it might work but you'd need a hardware platform you trust (one where you are sure no radio baseband processor is going to snoop at your memory any time it wants), use AOSP and then an open source app. Then also if there are any registration or routing services those would have to be open source as well.
