The problem with php is that there is no central registry where you can submit your own module like Ruby gems and npm registry for node.js. It feels like you have to reinvent the wheel every time you work on something new...
If you want to get your feet wet with a multi-user web application, I recommend trying Sonata's sandbox: https://github.com/sonata-project/sandbox#installation
Composer just happens to use packagist as a default repository. It alone is not a repository.