This might result in excessive implications (causing maintenance overhead) when further tags for the rest of the fairies are introduced. Same reason why Kancolle characters don't imply Kancolle (or other characters to their respective copyrights, for that matter).
Another issue is that a fairy might be portrayed as, well, a normal girl, instead of as a chibi fairy. Kouji already did this earlier with the Miracle Mallet.
Abyssals also don't imply the shinkaisei-kan tag either, for both the above reasons.