The answer is control over the width of line.
Cross hatching is a technique used to create shading and texture by drawing intersecting sets of parallel lines. While it can be done with a brush and ink, it is not a unique advantage of this medium, as it can also be achieved with pens and pencils.
One of the primary advantages of using a brush and ink is the ability to control the width of the line. By varying the pressure and angle of the brush, an artist can create lines of different thicknesses, allowing for a dynamic range of expression and detail.
While ink can be diluted to create washes that have a degree of transparency, the marks made with a brush and ink are generally more opaque compared to other media like watercolor. Therefore, transparency is not a primary advantage of brush and ink.
Brush and ink can produce consistent lines, but this is more characteristic of pens, which are designed to deliver a uniform line. The brush's flexibility allows for variation in line width, which is often more valued than consistency in this medium.