Rewinding is done professionally everywhere in the world, first-world countries included. It's very common, even my fairly small ex home town of 200k people had countless of rewind shops.
Obviously, in higher-pay countries, you won't rewind a $200 motor identically just to repair it, but you may rewind a $10000 motor for repair (costing significantly less than the price of the motor), or you may need to create special windings for special voltage requirements.
For large or special motors, winding at the winding shop is the same semi-automated, mostly by hand process as originally done at the factory, so it'll end up being cheaper than full replacement because a lot of the work (everything else except windings) has been already done.
For small mass market motors, they are wound by highly automated machines and it's obviously cheaper just to replace the whole motor. In third-world countries with cheap labor, rewinding them may still make sense, and I see this only being good (for environment, and the people can make living with it!)