The Common Application was historically focused on more selective private schools (the ones more likely to have more generous need-based aid). Public schools are relative latecomers to it. What that means is that The Common Application is a better match for more selective private schools (which tend to want essays and recommendations), while being less of a match for what many public schools look at in admissions (some of which do not use essays and/or recommendations, or want very different kinds of essays). Note that many more selective private schools do not have their own applications, but accept only The Common Application, sometimes along with other shared applications. In contrast, public schools are more likely to have their own applications, or use shared applications for schools within their own state.
It also increases the likelihood of copy-paste errors when entering the same information into multiple applications.