Foam compresses when impacted. Helmet impacts ground and compresses for simple example 3 mm of the foam on the outside of the helmet. Head impacts the inside of the foam and compresses for example 3 mm of the foam. The foam thickness between these 2 points is unaffected. If a cheap helmet has adequate thickness for there to be an area between these points not to crush, then making it thicker does not result in better energy absorption. If a cheap helmet is thinner to where there is no area between these points, then a thicker foam would be "more protection."
Better than thickness would be to change the material. EPP has much higher energy absorption properties than EPS. But if EPS is adequate in absorption properties for head impact, then a more expensive and heavier material still doesn't make "more protection." Thus, EPS is used in helmets for the weight property. At I am guessing less than $1.00/lb for EPS (I extrude, expand, and mold EPP and EPE, no experience manufacturing or selling EPS), you are paying for the shape design of the "better" helmet for the first 3, reasons listed above in Little Darwin's post.