The gemara quotes a mishna in Parah where the Tana Kama and R. Yehuda argue who is kasher for the kiddush (mixing ash and water) of parah adumah. T.K. holds that a חרש שוטה וקטן cannot do it, but a woman can. R.Y. holds the exact opposite, a woman cannot, but a child can. Regarding the machlokes of whether a woman can do it, the gemara says that they argue whether ונתן is meant to exclude ונתנה. But regarding the machlokes of whether a child can do it, the gemara says that they argue whether we darshen ולקחו to be inclusive, and therefore forcing us to include a child. It is understandable that R. Yehuda would normally exclude חרש שוטה וקטן from everything, but here the pasuk forces an inclusion. But why does he just include a child and not a חרש ושוטה? Tosafos writes: והא דמכשיר טפי בקטן במחרש ושוטה, יש לומר משום דאתי לכלל דעת. Since a child will out grow his לאו בר דעת status, it is more logical to include a child, rather than including a חרש ושוטה who are permanently fixed in their לאו בר דעת status.
The Chazon Ish (Parah 11:11) points out that when we include a child, we are obviously only including a child who is of age to make rationale decisions and would objectively be considered a בר דעת if not for the Torah excluding him. A child who is so young that he is essentially a שוטה would certainly be passul even according to R. Yehuda both for kiddush of the ash and water, and for the sprinkling. The machlokes is only about a child who has some level of intellect that we would consider a בר דעת in general - אלא שגזירת מלך הוא שאין דעתו מספקת במצות התורה אם לא היכי דאתרבי.
From the Chazon Ish it sounds like the real distinction between a child and a חרש ושוטה is that the latter are essentially not בר דעת, whereas a child has achieved some level of da'as that requires a גזירת התורה to consider insufficient for mitzvos. Therefore, if we have a pasuk we apply it to include a child faster than applying it to include a חרש ושוטה.
To me it seems that this approach doesn't fit well in Tosafos. If the advantage of a קטן is that he actually has a higher level of intellect that a חרש ושוטה, why would Tosafos write that his advantage is that he is אתי לכלל דעת, meaning he will come to be a bar da'as, rather than writing that he is included because he is already a higher level intellect than a חרש ושוטה. To me it seems from Tosafos that we are speaking about a child who is no more rational than a חרש ושוטה, yet we include him for kiddush since he has the advantage that he will become a bar da'as. The sevara seems to be that although he is no better now, it is a מום עובר, a blemish that will pass in due time. Since we are forced to include someone from the extra pasuk, we include a child.
Furthermore, we find that for other things we categorize a חרש together with a קטן and only consider a שוטה to be a real לאו בר דעת. The halacha is that a child can make a kinyan when there is a דעת אחרת מקנה, someone else giving it to him. The Rambam (Mechira 29:4) implies that a shoteh cannot make a kinyan even with דעת אחרת מקנה - see magid mishna. The Ketzos (243:4) assumes that a חרש is like a child who can make a kinyan with a da'as acheres being makneh, it is only a shoteh who is a complete non-bar da'as who cannot. If the Chazon Ish were correct that the present intellect of the child is what makes him stand out, we should have included a חרש together with him since for kinyan we assume them to have the same level of intellect. The fact that we don't include a חרש for kiddush implies as Tosafos writes that the advantage of the child is not his present intellect, but rather that we regard his lack of intellect as a temporary problem.