Use of white watercolour paint
Normally, in watercolour painting, you don't get any "white" paint.  The techniques for watercolour painting, as you stated, is to use the underlying paper to supply the "white" colour, and to supply for the brightness of a colour as you use coloured washes to allow the white to show through that layer's transparency.

However, there is a thing called gouache, which is a sort of opaque watercolour paint - and you can get white guache.  I've found white goache useful for adding tiny highlights such as the "whites of the eyes" and little stars and shines and sparkles.  It's also useful for covering up mistakes.  Plus, you can paint over the white goache with other watercolours.

The white paint you get in plain watercolours is mainly for making your normal watercolour washes a bit more opaque.  Watercolours are, by nature, transparent, so adding white to a colour will make them less transparent, but never opaque (unless you add gouache).  I would use white watercolour, perhaps, for example, for some leaves and foliage where you want the colour to be both paler and more opaque.  You still have to use layering though.

This page describes a bit of why you would use white watercolour paint - there are reasons to use white paint, you know.

This page describes how to paint "white" without using white watercolour paint - since people don't normally use white paint to paint "white".