In order to be able to install Moodle using Composer dependency manager composer.json in root directory should have some additional data. Now it used to declare Behat dependencies of Moodle itself. Composer uses tags so current mirror on github will work perfectly matching version tags. To work with branches it's possible to declare each MOODLE_NN_STABLE as special "continuous" version like 2.7.x-dev / 2.8.x-dev / etc. This means that you may switch between stability and declare 2.7 or 2.7@dev (see composer tutorial). Once composer.json updated everything will start working without need to cherry pick something.
Then command like this will fetch latest 2.7.x release and put it in vendor directory.
composer require "moodle/moodle:~2.7"
Next step is to configure how to expose the moodle core to serve. One way is to point web root directly to vendor/moodle/moodle. Another option is to use events like post-install-cmd to execute command that performs particular logic with sources. Actually there is one more option -- to develop own installer like it did Magento.
Why it is important? I see it mainly for automation. It would be tricky to fetch latest release in 2.7 branch using bash/wget. In same time it is easy to define particular version and stick with it. Composer comes with some infrastructure behind like Packagist. At the end of the day sources could be cached locally or fetched from github. This offloads Moodle servers and makes distribution more flexible. So far I don't see any disadvantages using Composer
There is an issue on tracker https://tracker.moodle.org/browse/MDL-48114 with pull request. I'm following Dan's advise and want to discuss this first to get an agreement. Please read the Composer documentation https://getcomposer.org/doc/.