Older stories in the fantastic tradition often feature a protagonist that is not of the fantasy world. Alice in Wonderland. A Connecticut Yankee in King Arthur’s Court. The children that travel to Narnia. John Carter of Mars. Occasionally, a more recent story will also employ this technique (for example, Terisa in The Mirror of Her Dreams), but in general this method is rarely used now. I believe this development is tied to the idea that fantasy settings should be complete within themselves and internally consistent; a replacement for reality rather than an interesting location meant to function as a stage.
Originally, the technique of taking a “real world” person and inserting them into a fantastic setting was probably meant as a way to help the audience accept the fantastic world by giving them someone familiar (the protagonist) to identify with. This structure also works well because as a visitor, the protagonist is not expected to already be familiar with the setting, so they can discover the setting along with the reader. John Carter didn’t get a setting background book when he was transported to Barsoom. This is a good fit for tabletop RPGs: no setting infodump assimilation required.
John Carter and Alice are both essentially planar travelers. This is also more or less what FLAILSNAILS characters are. I used to worry about making sure that all PCs “made sense” in the setting, but I’m coming to care less and less about this. The FLAILSNAILS conventions have taught me that my players can run whatever they want without messing up my campaign setting. My current players have been making characters using the online 4E character builder, which offers a huge variety of races, classes, and powers. None of them have made anything too exotic yet, but with this framework it wouldn’t even matter if they did. Just treat any odd PC the same way you would treat a FLAILSNAILS ConstantCon character.