How does my phone not set on fire?
"1A is enough to melt wires considerably thicker than those on the circuitboard inside my phone."


Are you sure?

In any case, the circuitboard wires are flat, short, and all thermally conducive to the board. Heat generated does not stay in a wire but is distributed throughout the phone and case. You'll notice the whole phone gets warm.

Discussion of required trace width factors at EEVBlog.