Cheresh, Shoteh, V'Katan in Shlichus

The Gemara in Baba Metziah 72a says that there is zchiya for a katan. That means that a gadol can be zocheh in something on behalf of a katan. The gemara says that the reason for this is "asi lichlal shlichus", meaning when the katan grows up he will become eligible to be a shliach.

Rashi in Baba Basra 156b says that this halacha is only midrabbanan. On a d'orayssa level there is no way a katan can have zchiya.

Rav Chaim in stencils, however, brings a Raavad that this zchiya is even on a d'orayssa level. Rav Chaim asks from the fact that most rishonim hold zchiya works m'taam shlichus (that the mizakeh is actually acting as a shliach of the zocheh). If so the katan is actually having the m'zakeh act as a shliach for him. This, however, is not possible because there is no shlichus for a katan. So, the question is, how can the Raavad say that a katan can have zchiya on a d'orayssa level?

Rav Chaim brings a Rambam in Mechira 29:11 as follows:

יא] ייראה לי שקטן שקנה קרקע, ונתן דמים, והחזיק--תעמוד בידו, אף על פי שאין ממכרו בקרקע כלום: שהקטן כמי שאינו לפנינו הוא; וזכין לאדם שלא בפניו, ואין חבין לו אלא בפניו.

Here the Rambam is saying a remarkable idea. If a katan acquires a field we say zachin l'adam shelo b'fanav and the kinyan works. The problem is that zchiya would usually mean that a gadol would do the maaseh for the katan and the zchiya would be that the gadol acts as a shliach for the katan. Here, the katan is doing the maaseh. So what is the zchiya for?

Rav Chaim learns from here that zchiya can also mean that we are mezakeh daas to the katan. This is not a zchiya of shlichus. Rather, it is as though impart daas to the katan where he doesn't actually have it. Since acquiring property is a good thing, we act as if the katan had daas and we allow him to acquire the property.

Rav Chaim says that this is also the pshat in Kesuvos on 11a where it says we use zchiya to allow a katan to go into the mikveh to be migayer. Again, isn't the katan doing the maaseh? Rav Chaim says the same idea, the zchiya here is only on the daas and is not working through shlichus at all. (See Tosafos there in Kesuvos who also deals with Rav Chaim's questions.)

With this idea, Rav Chaim explains the Raavad as follows:
The Raavad in Gerushin 6:9 says the only reason a katan cannot have a shliach is because the katan has no daas. Therefore, by zchiya we can be mezakeh the daas to the katan. Once he has daas we can then act as a shliach for him, even on a d'orayssa level. Rashi, on the other hand, in Baba Metzia 72a says that a katan is totally mufka from shlichus, from the pasuk of ish - prat l'koton. If so, a katan cannot have a shliach act for him in any circumstance, and the zchiya cannot possibly work on a d'orayssa level.

What about the other way around? Can a katan be zocheh for a gadol?
This is a machlokes Rashi and Tosafos in Gittin on 64b. Rashi says this can only happen on a d'rabbanan level. Tosafos argue and say the zchiya is even midorayssa. Tosafos there ask, how can this be? Isn't zchiya mitaam shlichus and a katan cannot be a shliach? Tosafos answer that the only reason a katan cannot be a shliach is because they have no daas. But, again, since a katan eventually will have daas its not a problem. This may be following the Raavad that we are mizakeh the daas to the katan. Rashi may argue that ktanim are totally mufka from shlichus, and nothing can be done to help. (Rav Chaim in zchiya and matana 4:6 discusses this Rashi as well.)

To sum up we basically have two mehalchim in why a Cheresh, Shoteh, V'Katan are not in the parsha of shlichus. One pshat is because they have no daas. The second is that they are mufka from shlichus from a gezairas hakasuv. The nafka minah is, in cases where you can "give" them daas can they be in the parsha of shlichus.

[More maareh mekomos on this topic: See Gemara Gittin 23a, Birchas Avraham on that Gemara, Kobetz Biurim Os 16. See also Kobetz Hearos Siman 5: 12, 13 that discusses a very similar issue regarding bnei krisus]