This doesnt have an effect on the hair path itself, but this comes into play if you use instances with your particles.

So for example you go to Particle Properties > Render > Render As : Object then children will use the Size and Random Size
Or if you use the Particle Instance modifier, that one also has an option to use the particle children size for its instances.

So, for the original report, I'd say this is not a bug, but working as expected.

I'd say documentation is a bit misleading here:
https://docs.blender.org/manual/en/dev/physics/particles/emitter/children.html

Children are Hair and Keyed particles assigned subparticles.

This is not true, children are for Emitter particles as well (2.8 is a bit misleading here since it will not display emitter children with any visualization type other than rendering as objects/collections -- but you can have children on a emitter particles...)

Children Size: Only for Emitter. A multiplier for children size.

This is not true, children can be on hair -- and size makes a difference here as well (see above)

@Aaron Carlisle (Blendify): maybe we should correct this?

Anyways, I think we have to close this, thx reporting anyways!