How does washout increase static pitch stability in subsonic swept wings?
Since its earliest days during the pioneer era, washout on a swept wing has been accurately described as "putting the tail at the end of the wing." It works in exactly the same way as a tail stabilizer.

As long as the change in moment of the rear surface is greater than the change in moment of the forward surface the plane will be statically stable. It matters not whether the tail is inboard, outboard, moved ahead of the wing (as a canard), tacked on the end of a swept wing, or even tacked on the back of a straight wing in the form of a reflex trailing edge.

On a straight, unswept wing washout can delay the stall a little, but stalling is a complex subject and best treated separately.