-- the superconducting magnet shell requires the accurate creation of 'nested doll' cryogenic containers, built to withstand magnetostatic forces in a highly regulated environment with defined safety requirements under catastrophic failure modes. Solving the design problem is equivalent to solving a huge set of nasty, coupled PDEs subject to loads of material constraints. This is directly analogous to aspects of jet engine design.
-- inside the bore of the magnet (but not in the cryostat) goes a device called the gradient set, whose job is to generate \partial B_z/ \partial_{xyz} as a function of time (that, very much indirectly, the radiographer specifies). This is a water cooled, resistive set of magnet coils with a defined frequency response curve, linearity requirements, etc. The current into them is generated by a set of three huge amplifiers, which have to actually take a signal delivered on a timebase of microseconds and volts and amplify it with negligible delay and deliver kA into a large inductor centimetres away from a patient. This is a formidable (power) electronic engineering challenge with huge parallels to various aspects of electrical engineering – e.g. managing (preventing) dielectric breakdown, thermal management, inverse solutions to Maxwell's equations in a quasistatic region (people use streamfunctions to do this well), etc.
-- the RF side of the system has to transmit kV and receive microvolts within microseconds into a definitively challenging electrodynamic environment with constraints on harmonics. Everything has to keep to a hard realtime constraint. The ADC must have a huge dynamic range and the problem is conducted massively in parallel. This is directly analogous to problems in telecommunications or RF design, but harder -- intermittent pulsed not continuous wave, and a hard requirement to accurately measure analogue voltages. Designing the RF coil ("probe" in NMR speak or ≈"antenna") is a further horrible (full-wave) EM design problem that even GE often subcontract out to one of about five specialist firms worldwide.
It's not a priori obvious to me that lots of competing companies would be better at creating stuff that requires the interaction of disciplines like this. Rather, I view the split up of GE and all of the woes of the article as evidence of a business mismanaged by MBAs. The defined benefit pensions should have been protected by law and overseen by an independent regulator - like my defined benefit pension that sits above my employer and shares risk among many different universities.
It wasn't until the 2008 GFC crushed GE Capital that it all started to really come apart, many decades after Welch got started.