Yeah, the physicality of fairies is not... how shall I put it... well, it's not a guarantee. As Greenfairy mentions, there's plenty of mythology on them alluding to shapeshifting, invisibility, immortality, etc. Moreover, there's also tons and tons of mythology about them not appearing as they are, or appearing differently, depending on the environment or 'realm', if you will. In other words, they may appear ghastly in our world, but more corporeal elsewhere (wherever 'elsewhere' is) or like, look more beautiful to us than they are in reality (glamoring). Is that not akin to god(s) and angels?
We often assume 'god' to mean the Judeo-Christian-Islamic god, but there's plenty of deities elsewhere who do have a human-like form, and/or have the whole glamoring, shapeshifting or invisibility thing going on for them, same as faeries do. The "cute stories" thing is another misconception; I personally think the fay are about as cute as we are. In other words, there's ugly and grotesque ones, wingless ones, cute-as-a-button ones, etc. There is no reason to assume they are good or kind; it's akin to an alien race assuming humans are inherently cute or kind. We have ofc lots of modern fiction depicting them as such, but people who look beyond the smoke and mirrors know it's silly to think the fay are cute little things about which cute stories are written.
...Sorry, I don't mean to derail the thread, I just find it illogical to assume unicorns are pure, fairies are cute, dragons are violent, etc. There's plenty of mythology suggesting the contrary, and since science can't prove their existence or lack thereof it seems queer to me to assume these creatures (be they real or not) are inherently... well, anything, really. To me, this is not unlike people assuming awfully good-looking people don't commit crimes ("but she's such a pretty girl! how could she have murdered someone?") and people who look like hobos are inherently guilty of something ("well he certainly looks like a dirty old man, so he must be bad").
EDIT:
I might as well point out that one of the reasons I don't so much believe in god(s) as I am rather apathetic about the whole thing is because... I don't inherently assume god cares about me or wants what's best for me, and it doesn't make sense to me that people do, either. "Jesus loves you!" ...Why?

This reminds me of girls confessing to me in high school. Why are you in love with me? You don't know anything about me at all. Tell me you love after years of living with me and putting up with my ugly bitch face in the mornings. Otherwise I am not at all inclined to believe you.
On the other hand, believing in faeries make sense to me because their existence (or non-existence) is not something that benefits me or them, nor is there an assumption that they care about me, or that I care about them. They simply exist, here or Elsewhere, and they're part of Nature as is everything else. Likewise, I believe in aliens. They, too, exist elsewhere, I don't know where or how or why, but their existence isn't necessary to mine, nor mine to theirs, they simply exist for their own sake, not for mine, and that's partly why I'm not concerned with finding them or them finding me.