My moto Z had same symptoms as Takeo Otani’s. Never over-used it, kept it cool, no drops, no scratches, clean USB port.
I am also convinced, bad battery was the problem: phone indicated a full charge after just 20 mins of charging. battery life just ~2 h in standby. Energy-intensive apps like camera, let phone re-boot. After rebooting a fully charged phone (over night), it was <30% charged.
MY BATTERY REPLACEMENT ATTEMPT TODAY BROKE THE DISPLAY, ALTHOUGH, I WAS EXTREMELY CAREFUL with plektra tools, hair dryer and suction pad, even dipped tools in isoprop, which helped a bit to “cut” the glue threads.
Half way of removal (>1 h), noticed a little thin crack (in the back-layer, from bottom-right corner to 2 cm above moto logo)
Took another 1 h, until front was removed.
Last switch-on try: VIBRATES, but SCREEN is DARK -> VIBRATE reboot loop. Dis/Re-connected display twice. no change.
MOTO Z NOT SERVICE-FRIENDLY AT ALL!
Not tried new battery! Will not buy new display nor moto!
BE MOST CAREFUL WITH BOTTOM 4 cm REMOVAL!