One thing that irritates me, and I have come across this (though not to date directly), is the assumption that fairies and fairytales are for kids and are "twee" bedtime stories. This tells me immediately whoever says this almost certainly hasn't read the original fairytales collected by Charles Perrault, Hans Christen Andersen and the Brothers Grimm. These stories are anything but twee! And certainly Disney could have not have shown The Little Mermaid as Hans Christen Andersen originally wrote it. It is far too grim.
But one aspect of Shakespeare's play, which the farce based on it also showed well, is that the Bard did not show fairies as twee characters, far from it. They are crucial to the plot. We see their weaknesses (Puck's mischieviousness, his enchanting the wrong man to begin with and so on). We see the feuding between Oberon and Titiana and while we might not be able to identify with fairy folk as such, we can all identify with feuding couples!
So if well rounded fairy folk characters are good enough for the Bard of Avon to write into his plays, they're definitely good enough for me to write into my stories!