Is there any advantage to the brush-only version if I do not need cables to pass front to rear?

Not much, for the job you have described.

If all of the cabling remains at the front and you simply need a horizontal route, the ring manager is the more purposeful choice.

The brush-only version earns its place when cables need to travel between front and rear, or when you reasonably expect that requirement later.

Buying the brush merely because it looks tidy would add a facility you are not actually using, and there is no virtue in making a rack more elaborate than the cabling demands.