The bent wheel is damage done after it was removed, and not the problem that caused your watch to stop. No watch would run at all with a wheel that looked like that. Possible it was dropped on the floor and stepped on or something.
The real issue here in this cropped photo I've made from yours:
You can see where the red arrow is, that a section of the wheel has worn and is quite a bit smaller than the section directly below the arrow. This whole section should be the same diameter, and should be a polished cylindrical shape. The wear here is obvious, so this is the problem that is addressed during the service, not the bent portion of the wheel.
This is a large amount of wear for just 4 months. I would typically see this sort of wear only after many years of service, running in a watch where the oils have long dried up. I suspect there is some wear on the upper part of the picot as well, above the bent wheel, but the angle of the wheel prevents me from seeing it.
Cheers, Al