How come English barristers have too-small wigs?

Like the one shown here: Cultural Flashpoints North of the Scalp - The New York Times

I can understand the idea of sticking with tradition.
And I can understand the point of the original wigs - you don’t want to fuss with your hair all the time, so it’s the easy way to keep an elaborate hairstyle.

But why don’t they cover all the natural hair?

I think the article you cited answers the question quite well,

CMC fnord!

Eighteenth-century fashions for men’s wigs came in every conceivable variety and often reflected the common trend for new fashions to react self-consciously against old ones. Too-small wigs were just the flipside of too-big ones.

Any style could have become associated with barristers. It just happened that it was this particular mid-century fashion.

Ede and Ravenscroft - Robe Makers & Tailors since 1689 - Legal [PDF]

They are symbolic and traditional rather than in any way functional. You could as easily ask why they cover any natural hair, as why they don’t cover it all.