It is pre-compiling apps from java to native executables. This comes from the ART runtime which is the default in Lollipop and newer. Google for "android ART"

I think this is a HUGE problem, and that somebody is going to die because they're unable to call 911 while the phone is "optimizing"

Allegedly in Android N this will be much faster. When I upgraded my Nexus 9 to N this step was probably less than 30 seconds long. I almost didn't even notice it.

Shouldn't it be possible to do this as part of the build process, or even by the play store?

Even during install time seems to make a lot more sense than after reboots!

It is performing AOT compilation. https://en.wikipedia.org/wiki/Ahead-of-time_compilation

The phone environment is not conducive to JIT'ing, unlike your typical desktop/laptop.

Then why on Earth is it doing it on restart?????