they tend to pitch up when you apply power.
Normally more a problem in the landing configuration missed approach ?
Generally due to what is referred to as the normal prop (or nacelle) force and, for some Types, can be a significant long stab destabilising input.
Mainly a concern with larger motors processing lots of air .. while seen often on the piston-to-turboprop conversions where the engine (and, hence, prop) is moved out forward for weight and balance considerations, the underslung turbofan is a contender with the force showing up at the nacelle inlet.
Sometimes the driver for incorporation of an SAS to modify the stick force characteristics.
Another result of the flatter CL vs AoA curve would be that a swept wing jet could develop a high rate of descent with a nose up pitch attitude
.. perhaps the Cd curve is the more relevant consideration ?