Even if the Tooth Fairy was real, how would she get her hands on real money? She’s a mythical creature who has no need for hard currency.
It would make much more sense for her to offer four-leaf clovers or shiny bits of stone or some bullshit like that.
And why do kids need to be incentivised to lose teeth? It’s not like it’s not going to happen anyway. Basically, we are rewarding kids for something they didn’t earn and is inevitable, just like the 27th place ribbon in a three-legged race.