Hi Owain
It is true that Newton does not really explain Lift, but it is a much less generic way of looking at it than Bernouilli, same as Newton laws give much more detail about a body going downslope than energy conservation law does.
Darrol Stinton has a very nice explanation wich put the focus on the air particles rather than the wing. That is the best I have ever seen because the order in which events takes place is the correct one, in my opinion. That is: the wing pushes the air, the air is not easy to be compressed as a result, but pressure changes will create pressure gradients all around the wing, and the air will flow from higher to lower pressure, and the resulting motion, if we look at Newton third law, reveals the existence of Lift and Drag. According to this, the pressure changes come first and the speed changes are a result, and not the other way round, as bernouilli's explanation suggests.
the faster the air is, the more accelerated it is
Why would that be?
Well, this one I must confess I am making an assumption. That assumption is that for a given set of conditions, the speed imparted to the air is a "given percentage". So the faster the air stream is, for that same "percentage" means that the air is imparted a higher speed. Something like: if airspeed is 100 kt, the air will be accelerated 10 kt (a 10%). If the airspeed is 200 kt, then the air will be accelerated 20 kt. Double acceleration, double force.
If I am not right, then there must be another reason why increasing speed increases lift, aside from more air being "processed" in a given instant. Otherwise speed wouldn't go squared.
I also hate the "theory" of the faster molecule above and the slower one below to reach the trailing edge at the same time, and I hate Koanda even more.