Looking at teardowns, like the one at ifixit [1], the touch id sensor seems to be a pretty standard imaging sensor that heads to an NXP chip. I'd be willing to bet that the encryption of the print happens on the nxp chip instead of the imager, so if the NSA/whoever were doing a "repair", they'd probably just put an MiTM chip on that insecure path for later playback. Against a state actor, Touch ID is a triviality.

[1] https://www.ifixit.com/Teardown/iPhone+5s+Teardown/17383

Maybe they want to move encryption onto the sensor chip in future generations, because the scheme you described is indeed a joke.

But to be honest, it's not like fingerprints are such a hard to obtain secret in the first place.

Hell, they could, on boot, display a message with something like "This phone contains contains a non genuine apple part"

Then the question is, could the NSA/CIA/etc trick the phone into thinking the repair was valid?

Almost certainly so. Decap the chip, pull the flash contents out to get the key, etc, flash a new backdoored chip, you're done. Hobbyists have been decapping chips and pulling flash for a while, so this is certainly not beyond the abilities of the NSA/CIA/etc. You wouldn't need the exact same make of chip, just one that presents itself as the same.

On boot? Many naive users never boot their phones after the first time they open the box.

So then, what, if not on boot, show it all the time, with no option to suppress? If you offer a way to suppress it, that will be used by the bad guys.

I say show a message whenever Touch ID is activated. Then again that would be really freakin' annoying. Still better than bricking the phone.