For the question "why would anyone want to work at GS as opposed to their clients", it's not a matter of the number of corporations, it's about the number of good roles.

A very large, say property developer, might hire GS for its fundraising needs, but a GS grad wouldn't want to work laying bricks. He might want to work as CFO or someone very close to the CFO, but those roles are much harder to get than working as grad for GS.

So it's not just about what the grad wants, it's also about what he can get.

This shouldn't be controversial. Anyone who's been in the industry knows that people move "up" from IB to their clients. Of course everyone wants that, but again such roles are harder to get than IB.