There may be some confusion present as there is both a Kitsune clan/family as well as kitsune spirits. The Kitsune family is absolutely a playable character type, whereas the kitsune spirits are just that; spirits of Chikushudo who, while they might visit, have no home in Ningen-do. The kitsune spirits are known to interbreed with the Kitsune family (who live in Kitsune Mori [Forest]) and the Child of Chikushudo Advantage that CatLord mentions is intended to represent just such a character.
As for why Naga and Nezumi (Ratlings) are represented as playable characters, the (very) short answer is that the Naga and Nezumi are purely MORTAL and as such are not meaningfully different from Rokugani (or gaijin) at a cosmological level. Even then, the stats are really meant to represent NPCs, as evidenced by the fact that all of the mechanics were are discussing are presented in "Enemies of the Empire", a book of potential antagonists. Even the sidebar on page 81, above the Naga creation rules says
The mechanics in Fourth Edition Core book are designed for Rokugani and are not ideal for depicting Naga.
Certainly you may allow Naga and Nezumi characters in a game, just as you may allow gaijin and the game will not immediately break.
The kitsune, however, are full-fledged spirits and, beyond some extremely specific techniques and plot necessity, arguably not subject to the game's mechanics some 99% of the time. In my experience spirits of all kinds are best handled in L5R when dice rolls come into play primarily to give the players information.
Meaning no flippancy in my response, I would posit that you would have the answer to your query by the simple expedient of replacing "kitsune" with almost any other spirit. For instance, "[Is there] a good reason why [fire kami] are not available as player characters?"