This debate comes and goes on pilot forums every so often
The wing produces lift
by deflecting air downwards. That is the most basic physical principle in play. The lift is the "equal and opposite" reaction to accelerating x kg of air per second downwards at y m/sec.
It's true that the pressure above it is lower than the pressure below it but that is a consequence of deflecting the flow
You can't have one without the other (in any fluid).
If your objective was instead to just make something that produces a pressure difference across an object, the result would inevitably be a deflection in the airflow...
The wing being an "aerofoil" is of secondary importance. An aerofoil is a more efficient (less draggy) way of deflecting the airflow. Otherwise, if you don't mind the drag, a barn door would do as well.
This is basic Newtonian mechanics. Bernoulli merely worked out some equations which simplify Newton for working with fluids, to an extent that makes it easy to work out flow in pipes etc. But if you applied Newtonian mechanics to each separate molecule in the airflow, you would end up with Bernoulli's equations
The two are just different ways of looking at the same stuff.
Then, people worked out convenient mathematical treatments for some of this stuff. Like the circulation theory for example. If you integrate the little bits of airflow around a wing you see a net "circulation" around it. But this doesn't mean the air
actually circulates
It does that only at the ends (wingtips) where the vortices come off.