Im not certain on that, but i believe it may be related to damage concerns regarding the accuracy of the touch screen response/ reaction which could be damaged from too much pressure on it, etc.
Also, ive known many people who game excessively, their hands got warm and this causes noticeable friction that could be damaging to it. Remember, Nintendo touch screens dont have the same inpuy response so to speak that android/ IOS tablets do and because of this things might get a bit awkward if you do that too much with your fingers on a 3DS screen... Im not definite on this, but i believe it is likely why Nintendo advises such. I cant say though even if this is why if its always 100% true because it seems people here (a lot of them i noticed) use their fingers and i dont remember hearing of any problems that occured later on with the touch screen from doing that excessively.
Just what im guessing their reason is, hope this might answer your question.