Pitch would have to be decreased, not increased, to maintain AOA and speed stability. That means that altitude is sacrificed.
If you want to maintain altitude in a bank, total lift is increased (to maintain a constant vertical lift component) therefore AOA is increased.
If you want to bank, you have to choose between giving up altitude or stall margin. You can't keep both.
Last edited by Vessbot; 11th Nov 2017 at 05:21.