Speaking as s songwriter, primarily, my observation is that formal music education and a deeper understanding of music theory leads to writing music that's more complex. That's not necessarily inherently a good thing nor is it a bad thing. It depends on who's doing the writing.

Example: Billy Joel has a solid understanding of music theory that goes way way way beyond most songwriters and rock/pop/country/etc musicians. As a result, take a look at a chord chart for one of his songs -- very difficult to play. But it doesn't sound "pretentious" (unless you count his classical piano album, that is)

On the other hand, JD had almost no understanding of music theory, is my understanding. His songs are much easier to play in terms of chord progression (although if you play them the way he did, they are crazy hard because he was a phenomenal guitar player). Same with Bruce Springsteen and probably most of our collective inspirations and idols.

I think it depends on the person. I don't think JD (or the Boss) was hampered by his lack of music theory education, and I think that Billy Joel would have written iconic songs either way.

Caveat: In my experience, writing on piano also results in more complex compositions becasue it's so much easier to reach for all those crazy chords. Given Billy writes on piano, that may be as much a reason for his complexity as his knowledge of music theory.