With regard to Bernoulli: he's basically saying that there is energy added to the system and Bernoulli describes the conservation of energy for a system (where energy is neither added or subtracted from a system) so Bernoulli doesn't apply. Bernoulli is a mathematical description of an effect that happens in a closed system.
Consider the dynamics happening on a pool table. If we simply ignore friction, we can make extremely accurate predictions of the behaviour of the balls using the conservation of momentum and energy. And that works because friction is low compared to the other aspects of the dynamics.
But hold on! The balls are rolling, not sliding. So there must be friction, right? Oh dear. The laws of conservation of momentum and energy can't possibly be used to explain the motion of the balls because it's no longer an energy conserving system. And yet still, we manage to direct the balls to the pockets with unfailing reliability. How can that be?
Consider the dynamics of a wing. If we simply ignore viscosity, we can make extremely accurate predictions of the behaviour of the wing using Bernoulli's theorem. And that works because viscosity is low compared to the other aspects of the dynamics.
But hold on! We need some viscosity for the Kutta condition and to explain the boundary layer etc.. So there must be viscosity, right? Oh dear. Bernoulli's theorem can't possibly be used to explain the motion of the air because it's no longer an energy conserving system. And yet still, we manage to predict the lift coefficients with unfailing reliability. How can that be?