Not quite true, many aircraft have pitch changes with a change in thrust. This is due to the centre of thrust being above or below the centre of drag/gravity. This doesn't make them unstable, continuing to change pitch once the change in thrust had happened would make them unstable.
The issue with the Max is that at high angles of attack the control force needed to increase pitch decreases due to lift from the engine nacelles. Which means if you hold the same back pressure the aircraft will continue to pitch up rather than stabilising at a new attitude/speed combination. This makes it unstable, and also required MCAS to meet certification requirements.
The Max actually has fairly benign flight characteristics until you get near the stall.