The main reason for the recommendation of running Transmission as its own dedicated system user rather than your user is that, if the software has a vulnerability that allows exploits that will expose files outside of its configured directory, then it will not end up exposing the possibly sensitive files from your home directory, since Linux itself will prevent that kind of access through the basic permissions.
In order to make it easier to manage the files in Transmission's directory with your regular user, you should consider adding your user to the
debian-transmission group, which is the group that owns the files in the Transmission directory, and has (or at least should have) read/write access to that directory and the files within it.
The Ubuntu howto suggests this command (slightly adapted to get your user from an environment variable):
sudo usermod -a -G debian-transmission "$USER"
(Remember to log out and log in again after running
usermod, as it will not affect the groups of any existing process.)
Hopefully this will make it easier for you to manage the files downloaded with Transmission, while still keeping it running under its own dedicated system user, for better security.