As a surface-level-understanding layman myself, what about this is wrong? The 737 MAX is unstable, no?
No, it's not unstable. The 737 Max exhibits stable pitch behavior along the entire envelope. A lot of people think "unstable" means "it crashes" but these terms have precise meanings.
The 737 Max is a stable airplane. One of the problems it exhibits is that with increasing angle of attack, the stick force does not increase (linearly is the requirement, I think, I'm writing from memory here).
The way you know this is because MCAS moves the horizontal stabilizer directly, and not the control column that the pilot is holding. An anti-stall device like a stick pusher or a stick shaker provides tactile feedback to the pilot via the control column. Moving the horizontal stab directly is (basically) altering the trim of the aircraft. Thus it is a handling-qualities system.
It's not just a cost saving measure.
MCAS was a sound concept. It's implementation, however, was not sound at all.
As far as MCAS goes, in my opinion Airbus got it right already in the 80's in their A320 with their flight envelope protection.
Yes, it would likely have been safer if the 737 Max worked as expected by the pilots flying it.
That only works if retraining is not actually needed. Boeing's own test program gave adequate (but undisclosed, at the time) information for an independent observer to conclude that this was not the case here.
I've never understood why the fix wasn't implemented in the elevator feel computer. Except perhaps that it doesn't have AoA inputs and it's an old hydroelectrical system for which there may be a lack detailed knowledge.
This is part of why the MCAS could not be decoupled from the flight computer as I recall. If you turned off MCAS, you'd be non-compliant in the wind-up turn flight regime, and when coming in on final if I recall correctly.
So in aerodynamic parlance it is stable, but with disqualifying flying characteristics that had to be mitigated via a gadget whose nature, failure modes, and existence was largely hidden from the pilot, and downplayed in the FMEA/FMECA. (Failure Mode, Effects, and Criticality Analysis)
This downplaying was specifically intended to keep regulators from stipulating enhanced training for pilots. Thereby saving money.