I’d say that 200,000 is very very much an under estimate. A brushless DC motor, (which I am assuming is what is used, as it is a very cheap option for electronics like this) should last an awful long time.
Images shown here show the internals of the Pan and you can see both motors. The first page shows the rotation motor and its gears. Though they aren’t the best pictures and you can’t count the teeth, they don’t look like too large of a gear ratio, maybe 4:1, so they don’t have to do much to step the motors RPM down to the advertised ~20RPM of the camera. (These pictures make me want to pull my camera apart just so I can count the teeth myself! :D)
WYZE PAN INTERNALS: https://fccid.io/2ANJHHWYZECP1/Internal-Photos/Internal-photo-3777255.pdf
Also, while I was digging through this internet rabbit-hole, I found the iSmartAlarm cameras, which may be a surprise to most. This company uses the same hardware as the Wyze cameras, but seem to be originally designed to use with a DIY home security system. (They even have a BLACK Pan, but $70-$170 (depending on sales) more than a Wyze)
iCAMERA KEEP PRO: https://www.ismartalarm.com/devices/cameras/icamera-keep-pro/isa00023.html
But the point I was trying to make with the iSmartAlarm system is their version of the Pan hardware was released in 2015, and a brief search of the iSmartAlarm forum doesn’t bring up any topics about a dead motor. (Same with a google search)
iCAMERA KEEP 2015 REVIEW: https://www.cnet.com/products/ismartalarm-icamera-keep/review/
So its my opinion that the rotation motor in the Pan should last more than 92 days of continuous use.
However, the Pan is only about 50 days old, so might have to revisit this topic in another 40 days