The refusal to grow up will always be an enduring theme. The Romantic poets (particularly Wordsworth) explored this in detail in analogous relation to a more rural and simplistic existence, but also a reluctance to assume responsibility. As society and particularly industry and technology progress, we get further from a simplistic view of the world. In a much more general sense, the refusal to grow up is just a plain old fear of death, getting old, sick. Peter Pan is particularly applicable to the dread of growing up and facing the repetitive existence (reference to Hook’s ticking clock) and mundane jobs. Reluctance to grow up coincides with reluctance to accept certain inevitabilities like death and taxes. I think you’ll find the themes in Peter Pan can be applied in almost any novel, play, film which depicts the bleakness of existence in modern times, with an example being Office Space.
The avoidance of responsibility is also a recurrent theme and has philosophical significance in the works of the Existentialists and Absurdists for whom responsibility is a fundamental element of our own free will. Psychologically, the play is also exploring roles of motherhood and fatherhood. Philosophically speaking, the idea of responsibility is inborn; we are responsible for our own actions. Denying responsibility, via the so-called “Peter-Pan complex” is deny the inevitable just like denying growing old.
Another aspect of this play that I think will always be enduring is the idea of retaining a childish innocence, wonder and imaginative ability about the world while growing up and assuming the responsibilities of an adult. Easier said than done.
There is also the odd idea that as children grow up, the knowledge they gain can actually corrupt their imagination. This is one side of the coin since knowledge can also lead to broadening the mind. But the theme in the context of Peter Pan, is that imagination is even more primal than responsibility or any cultural ideas about ‘being a grown up,’ and that imagination (while not totally limited to children) is an element that is imperative for a child’s dev elopement.
But to go back to your question, modern elements are about avoiding the interpretation of a bleak, repetitive world of adults where you must act certain ways; and this prospect limits imagination and possibility.