Synchronous as well as Asynchronous (no magnet) motors are both very durable. We're talking hundreds of thousands, if not a million hours of operation (according to Tesla that's 60,000,000 miles at 60mph). If we don't throw away the motors with every car purchase (which is a big if in today's world of yearly disposable smartphones). Then even a small efficiency advantage should be immensely useful over the life of the motor. IIRC we're talking about 10% more efficiency for synchronous. If you drive it for 1,000,000h and use about 20kW in average operation, that is 20,000,000kWh. 10% would be 2,000,000kWh. That's significant.
NYC has a peak demand of 14,500MW (see here: http://blogs.ei.columbia.edu/2015/09/28/how-much-energy-does...). So you could power NYC for 8mins at it's peak usage with these lifetime efficiency savings(again it's unrealistic that the motors will actually run that long in cars, but at least the rare earths could be easily recouped when recycled properly).
So the motor is one of the places where an initial investment in rare earths, could be paid off easily over the lifetime of the motor. Assuming that motors aren't disposed of.
The batteries still require massive amounts of rare-earths though, and they don't have the same durability. I see much more of an environmental disaster coming here.
The auto industry heavily recycles. Pretty much every major part costs extra if you don't return the old "core" so it can be re-manufactured. Autos are stripped down before the frame is crushed. Not doing so leaves money on the table. I don't see EVs being much different.