The Kutta condition is insufficient to describe lift in all regimes (e.g. when the trailing edge of the wing isn't that sharp), but fundamentally you do need to fall back to certain 2nd law / boundary condition rules to describe why an airfoil generates lift, as well as when it doesn't (e.g. stall).

There's nothing in the Navier-Stokes equations that forces an airfoil to generate lift - without boundary conditions the flowing air could theoretically wrap back around at the trailing edge, thus resulting in zero lift.