, and are designed to weaken . This is a basic driving tesuji pattern.
Connecting in the centre next is expected next from White, for some thickness.
If White connects at , is double sente or close to it.
This seems better for Black than the official solution.
Black does better to atari at . I think that, in general, this is White's best response. Having no defect in White's wall looks to be worth more than the the few stones that Black picks up.
Charles For a standard of comparison, one can use the joseki sequence at pushing battles in joseki 2. In that case Black does much better for territory. It isn't unfair to compare that type of result, in which Black ends in gote, with this one, where Black has sente. The local tally turns out to be the same: Black had four stones to White's three in the initial position, before Black cut (the position comes from a Chinese formation, or conceivably a tenuki joseki). That all goes to show that Black's stone on the side has become a waste.