Thanks for the awesome video.
It's not the wire that's precise here - it just provides enough force to get a the stamped metal piece over the tooth of the plastic gear, then it slams into a hard stop, then the button batteries dump current into the other wire, which pulls it the other way, pushing the gear one tooth width, and slamming into the other hard stop. Each back and forth ratchet of the tooth turns the worm gear on the plunger the precise 0.05 units.
Another cool part of these is the initial insertion - there's a huge torsion spring that stabs a hollow needle into the skin then fully retracts it, leaving the rubber tube.
Then there's a little corner of the PCB with a cutout and power trace, you can stab with a paper clip to disable the pod in an emergency.
Then there's this membrane that equalizes the air pressure in the pod if you're flying with it. It lets air through but not water. So you can dive in a lake with it too.
I love clipping these things open and just marveling at the clever engineering for cheap mass production of such a sophistocated device.
Regarding price, my point still stands that wire is not cheap enough to motivate its use. Your link actually proves my point (1.6 USD/30cm). Pager/toy motors are costing cents.
But maybe it is more expensive. Then they probably choose it for the reliability, and a simple and quiet design. Or perhaps the button batteries don't have the energy to drive a pager motor.
While the pump manufacturer just puts a 1000m spool in his assembly line every few hours.
If you can design the wire to require 3x less material than the motor approach, it will win.