As you bank the rising wing will create more lift, the descending wing less lift that will mean that you will require more pitch to maintain level flight and with that extra pitch more drag.
Applying rudder in level flight will cause a yaw and the nose to turn around the centre of the axis of that yaw that itself will cause one wing to slow and the other to speed up again causing the aircraft to initially pitch up which followed by an increase in drag will then cause the aircraft to pitch down for a set level of power.
Pace.
I'm with you in your first paragraph. L emphasizes the need for back pressure when turning - which we all know. Back pressure also stops slip (according to L.)
I don't quite follow your second para. Do you mean "level flight" as in "straight and level" or level flight in the turn? The nose will indeed turn around the centre of the axis of the yaw - but when the aircraft is banked at say 45 degrees that axis will also be at 45 degrees and the turn will be earthward. Thus the tendency for a steep turn to increase it's angle of bank and also descent.
That is my own summary of what L is saying and it makes sense from my own experience. Probably that is what you are saying but perhaps in a different way. As L would be the first to point out the aerodynamics are not that simple, but it does indicate what one would most often expect.
I think most would agree that a high angle of attack combined with a lot of rudder is not a good idea.