A few reasons:

- There's one widely accessible database where resumes can be found. Since many people want to be found by prospective employers, this gives them an obvious place to put it.

- The resume format can be standardized, so you can focus on meaningful differences instead of the cognitive challenges of extracting meaning from a heavily stylized document.

- There can be a commonly available API for exposing this information e.g. in job applications (see "Apply with LinkedIn", which does exist).

- Because it's a centralized database, it's more up-to-date with professional developments and changes of contact information.

Not to say that it has to be a single company, let alone a linkedin-style company, maintaining all that infrastructure. But there is definitely value to a standardized infrastructure, and a company like LinkedIn seems to be a pretty successful way to build that.

There are just as many benefits to a standardized infrastructure as there are downfalls caused by adopting the wrong standard, by forcing people onto it, or by using it for too long.

Wasn't that what the whole LinkedIn "I vouch this person knows X" was supposed to be about?

I assumed that was basically for the purpose of ignoring your resume and selling recruiters a more accurate social graph backed summary of your skillet.