Probably not, in most cases. For the average user, accuracy and relevance are more important. Information overload is part of the problem.
Common queries result in tens or even hundreds of thousands of hits.
The ability of SEs to separate out the good stuff and list it first is more important than conducting a comprehensive search. Unfortunately, relevance is an extremely difficult concept to pin down. Ultimately, only the person seeking the information can determine what is relevant and what isn't. No set of machine instructions can make that determination with anything close to 100 percent accuracy. Nevertheless, SEs have made significant progress in this area.