“It sounds like the software itself is only there to cover another design flaw of the nose tipping up unexpectedly on take off”
The nose tipping up at take off isn’t a big deal. If the pilots had direct control of the plane at take off it wouldn’t qualify as any sort of design flaw.
The problem is that the computer is in between the pilots and the control surfaces.
And it is incorrectly interpreting the nose tipping up as a “stall”, so it goes nose down to pick up speed. That could make sense if you were at 20,000 feet and the plane’s nose tipped up. When you are just taking off and have no altitude to spare that’s a disaster.
The problem isn’t the plane’s physical design or the pilots, it’s a badly designed computer program that has more control of the plane at take off than do the pilots.
I agree that the software shouldn’t have more priority than the pilots. I don’t think any autopiloting should cut in automatically at all. If the plane’s behavior is so erratic as to require it, then there’s a problem with the aerodynamics of the plane itself. In this case it’s so slight that it’s not even needed.