In the song circles I go to, there is usually almost a group orgasm over simple "beautiful" melodies--usually 3/4 or 4/4, slow to moderate tempo, and only about 4 chords. I think these tunes are pretty, too, but I notice with most of them that they are not "catchy" in the sense that I can distinctly hear the melody in my head after I leave the session. One reason is that they tend to be very similar to each other. I start singing one melody and it morphs into another of the same genre.
[You know the old saying that there are only two Irish (or C/W) melodies--a slow one and a fast one.]
The melodies I write are (deliberately) a little less predictable, though usually not terribly complicated. Often I get the feeling, when I introduce one, that their very novelty is grounds for a lukewarm reaction. [My tastes in other people's music are not unusual, and I don't write melodies I don't like, so I have no reason to think they're just bad melodies.]
I don't know if this is what you folks mean by "tune burnout." I'm referring to melodic phrases and patterns, not specific songs.
One thing that made Paul McCartney (and the other Beatles) so memorable as a songwriter is that the tunes don't all sound like each other or like other "pop" or "rock" music. Unfortunately, "folk" songs tend to have certain very predictable chord patterns, just as C & W does, etc.
Anyway, I welcome tunes that are really memorable. When a really new one does come along, it's kind of sad if everyone (understandably) mimics it for their own songs.

Genie