Ultimately, formal structure is how the music is presented. If that structure is not effective, then the song cannot be effective, regardless of all else. Furthermore, music is ultimately a story - not necessarily narrative (though it certainly can be), but just like a movie or novel, it needs structural landmarks - both on a macro scale (a beginning, a middle, and an end), and on a micro scale (phrases and sub-phrases). Without such landmarks the material is simply presented as a string of successive events that may or may not have any relation to that which came before it or that which will come after but instead just like a Benjamin Franklin run-on sentence it keeps going and going and going like the Energizer bunny and eventually gets very tedious to read or write or listen to and incredibly difficult to understand what the author or composers is trying to convey. Just as sentences need punctuation, and films need scenes, and novels need chapters, music needs similar structure to effectively articulate meaning.
The basic goal for a composer, then, is to keep the material similar enough so that it clearly belongs together, but different enough to avoid monotony. A succession of apparently unrelated material will be appear abstract to a listener, while a succession of entirely unchanging material will become predictable and eventually boring. A major component of compositional skill, then, is the ability to balance the two. And one of the best ways to achieve that balance is through the formal structure of the song. (Of course, other parameters contribute to this story, harmony being the most obvious.)
The bottom line is this: How something is presented is often just as important as what is presented. And analyses of formal structures illustrate that "how".