The complaint "we can't spend the time to train new employees" isn't specific to the medical field, but the solution is the same: they can't afford NOT to, and the lack of staff is proof of it.
The last plan ended in the failure we're at now (no staff available to train new staff). The best time for staff to start training more staff was before they ran out of staff. The next best time is now.
The rub is that lack of staff isn't what prevents this, nor is even lack of staff time. It's a conscious, short-term-focused decision by hospitals to focus efforts outwards on making more money, rather than inwards on training or changing the status quo. And honestly, the long-term herculean task of changing the existing resident system seems, in my opinion, out of scope and fantastical for the average hospital.
Shadowing/Interning is already done in your MD program.
In Engineering, you will generally have 1 engineer paired with 1 intern/NCG. In a hospital setting that is an unrealistic ratio given the relative lack of staffing.
Add to that liability related issues because unlike CS, you as a medical professional can be held legally liable. This of course leads to high malpractice insurance rates subsidized by the hospital, who then in turn also need to show insurers that they are doing the needful.