Viability of Magnetically started engines
Three things come to mind:


Magnets are heavy.
Not all compressor and turbine blades are ferro-magnetic.
The starter would only start the engine, and then be dead weight.


Usually, new designs are implemented when they have clear advantages over previous solutions, but I cannot see what problem this would solve. The APU is a very versatile and lightweight piece of equipment that can power up all of the systems of an airplane. Not really anyone's prime target for replacement, I reckon that captain Sully would agree.