The plane is not unstable. A pilot who is trained for the actual flight characteristics absolutely can handle the plane. The problem is they weren't required to get that training, because 737's still all share the same type rating as if they all have substantially the same flight characteristics. Which is generally true except one particular attitude, high angle of attack.
It's an open question to me (I'm no one, but I am a pilot and a flight instructor in a previous life) exactly how different stall avoidance could be with MCAS disabled (which is indirectly done by setting stabilizer trim to cutoff) once it has already induced a dive by having fought with it a little bit too long. If it's a normal procedure to disable the very software abstraction that means you don't need a type rating for this airplane, but the stall avoidance technique is substantially different from other 737s - that's very concerning to me. Not that the plane is unstable or unsafe. But that there's a disconnect in pilot knowledge and actual airplane flight characteristics with this abstraction turned off.
Before fly by wire, it was always worth going for stability because pilots couldn't fly unstable aircraft. Fly by wire enabled making flyable unstable aircraft, and so trading off some inherent stability for more maneuverability (military) or higher efficiency (civilian) became an accepted design option.
In the case of the Max8, it's always on and there is additional training needed to react quickly when this happens. I think all current pilots who are watching this situation should know what to do at this point, but the needed the awareness brought by the situation. In the two crashes so far, it seems like the pilots had years of commercial experience.
On another note, I don't think the 737 Max is inherently unstable, so I'm not even sure this line of reasoning applies at all or even in part.
I suspect the blame lies with Boeing's management and with the FAA for being complicit with Boeing.