To me, the recruiter is representing the company. If they're reaching out to me, I'd like to think I already have an "in" with the company. Why would I circumvent that and go in alone?

Salary?

Because the recruiter gives names to the company of "here are the people I gave your contact info to" and the company makes sure that those people only go through the recruiter.

I've had recruiters tell me right upfront which company they are dealing with.

I'm not sure I see the incentive in me doing that...?

Unless, of course, I hate dealing with them. In which case I'm not going to get hired through them in the first place.

Why would I do that?

if they are exclusive to that client for that job, they will tell you the company name..

HINT, you want the exclusive recruiter..