Comment by kelnos

If you look at it as a tool for recruiters, you won't be searching for specific people. You'll be searching for attributes/skills you're looking for, and then get a list.

If you're an individual applying for a job, you'd link to your profile, so the recruiter who receives your application won't need to search.

If you're connecting with someone you know personally, then you should already have enough information at hand in order to know you have the right person based on their listed work experience.

The only time you might search is when you're doing professional networking and only have a name. But you usually have some other piece of info, like the company they work for, and possibly their broad job function or title. 99% of the time that should be enough to disambiguate people with the same name. And if all you have is a name, maybe you haven't really "networked" with them enough to warrant a connection?