Would it be easier/faster? Depends on a number of variables really.
My personal rule of thumb is to do what I feel most comfortable with. For me, a database "feels" like the best fit here. Plus, if you are tying responses to user accounts, then it affords some additional security benefits.
Also, as you say yourself:
I am concerned about my methods, particularly because it relies on writing the comments to .txt files, which requires a directory be readable, writable, and executable by everyone.
Depending on how far you intend taking this project, might you consider implementing different drivers? That way you could have (perhaps) a flat/file (XML based?) driver as well as a database driver (which might itself utilise a SQLite driver, MySQL driver etc).
Just some thoughts.
But, basically, I for one would utilise a database.