Now, I don't want to bore you with literature theory and stuff like "omniscient point of view", but I'd like to have a closer look at songs.
I As A Protagonist
The I-perspective surely is the most commonly used perspective in pop music. Of course, because the songwriter tells about his own adventures or interests (for example, "I Want To Hold Your Hand" by The Beatles). Nonetheless, telling a story that (almost) has nothing to do with you from I-perspective, can also be useful and interesting. Ultimately, you can take on a role and make the protagonist's emotions and thoughts more comprehensible. That the singer/the songwriter isn't identical to the narrator, can be made obvious ("My Name Is John Lee Pettimore") or not be picked out as a theme. Think about, what may be right for your song, but don't worry about any misconceptions.
What I mean by this is the following: Recently, a friend of mine auditioned a song about a guy who falls in love and then embarrasses himself multiple times. A funny song with good ideas but I asked myself "Why should I care about the story of a guy I don't even know?" I asked my friend if he would like to present this song from the I-perspective. He told me, he didn't want the people to think every word of the song was true.
Fortunately, I could convince him to perform his song live from the I-perspective of course, the audience liked it much more, because the song was now self-ironic, instead of making fun about another person.
Therefore my tip: You are only bound to your song! If your vanity stands in your way, you picked the wrong field of activity. On this topic, I'd like to cite a nice sentence, I heard from an American Folk singer: "Folk musicians are using themselves to present the song Pop singers are using the song to present themselves". I mean, at least in this regard, we should stay closer to the Folk basis.
Where there is an "I", there commonly is a "you". This is good, even though the effect of the listener feeling addressed, isn't there in most of the cases (except young girls listening to Justin Bieber). This stylistic device is just heard too many times. However, "I will always hold her hand" or "I will always love him" wouldn't have the same effect. So using the direct address in a song has no disadvantages but many benefits. This, certainly, doesn't have to happen with "you. Bruce Springsteen and other artists have often very successfully addressed a greater instance like "sir" or "mister". In his song "Martha", Tom Waits appeals to a woman of said name, making the listener think that he is attending a very private conversation a great way of writing songs!
That's why you ask yourself if the "you" you address in your song, can be substituted with your desired partner or if you can get a better idea. If your song is a conversation with your father, a judge or a neighbor on a train, your story gains a depth that can be very interesting. Or maybe a song that didn't need a direct address, now gains originality and effect. Try it!
From The Distance
Of course, the I-perspective is bounded. The I-narrator can (and should) only tell about his adventures and feelings. For this reason, it can be interesting to narrate from another perspective. This can make some stories more haunting. The song "Deportee" by Woody Guthrie tells the story of a plane crash many people died in. In the newspapers, there was mentioned that these were "only" illegal immigrants being deported. Woody comments on this by giving these people names. Why he doesn't tell the story from the I-perspective? Well, for him it was about raising empathy for the deceased. If he wrote the song from the I-perspective, this song would be close to a lament. He would literally beg for empathy instead of raising it naturally. Furthermore, the I-narrator would be a survivor or a dead person. The latter is not very uncommon in Folk songs but still quite a challenge.
What do we learn from this? If you are not the I-narrator, your song should be about one or multiple persons. Also, it is your task as a songwriter to make your songs interesting for us. Give the listener the chance to either identify with the persons or to raise other feelings for them, give us a name or other attributes!
Remember that unlucky fellow in my friend's song? He was just "he" or "the guy" If not even the songwriter doesn't care for that guy, then why should we?
I As A Minor Character
It is an interesting solution not to make the I-narrator the protagonist of the song. Instead, the story could be connected to the protagonist by being told from a friend's, foe's or another one's point of view. This makes it possible to keep a certain distance while still being able to convey your own impressions.
An example from my experience: Moved by the book "The Executioner's Song" by Norman Mailers and the movie "Dead Man Walking", I wanted to write a song about the death penalty in the USA. Telling in the I-perspective, how I wait for my execution, seemed arrogant and just not original to me. Also, there was the danger of the song being too moralistic and lamenting if I wrote the song from a very distant point of view.
A better idea was to write the song about a guy, whose former boyhood friend became a murderer. This gave me the chance to raise empathy for the killer on the one hand (because, in his early days, he was a nice boy and the best friend of the I-narrator), but on the other hand to keep a certain distance (because the I-narrator didn't see his former friend for a long time).
As you can see, the choice of your narrative mode is always influenced by your song. That's why you ALWAYS have to ask yourself if you chose the right perspective for your song or if it could benefit from a change.
Of course, I didn't tell you about all possible perspectives. Pets and objects (for example, walls and pistols) can also tell a story. Not everything that is original and imaginable, does make sense. However, it can never be wrong to make experiments. I hope you got some fresh ideas. Good luck for your songwriting!