"In reality, a bad song performed well will get higher marks than a good song performed poorly..."

Yes, I think I'd agree with that. From the thread title, it does seem that Johnny J IS talking about song-writing competitions.
In some competitions it is stated that the the judges NOT judging the performance. But if the song is perfomed competently and confidently, and with conviction, it must surely help.

In the recent Edinburgh competition, the top three places were taken by very well-performed songs, and the top two had a degree of musical arrangement with instruments other than the usual combination of solo voice and guitar. This certainly enhanced the overall feel, but if anything, made it less likely that one would pay full attention to the lyrics. However, I made myself listen to the lyrics, and they were also very good, and it seems it was the lyrics which "sold" the third placed song to the judges.

As a songwriter myself, I would sometimes appreciate a bit more feedback about what was thought of any song I have entered, tho' I would not necessarily want the judges to go through each one publicly.

At another club I go to, the competition is decided entirely on an audience vote, and somewhat amazingly you CAN vote for yourself, tho' I would never do this.