Originally I wrote at the end of note 4 of Tosefta 2:6:
I was not able to find another suggestion for a reason for this law or come up with my own.
I have changed that to the following:
I would like to suggest a practical reason for this law that does not stem from any verses. The key difference between Peah and Leket is that the minimum and maximum amount for leaving Leket is well defined where as for Peah it is not. Dropped produce is considered Leket if and only if it is either 1 or 2 stalks. If it is 3 stalks or more then it is not Leket and it belongs to the owner. See Mishna Peah 6:5. Therefore when a poor person is in the field collecting Leket he can clearly see whether 1 or 2 stalks have been dropped or more and therefore there is never a doubt in his mind whether the owner intended to leave this produce as Leket or not. However by Peah the minimum amount is not well defined at all and the maximum amount does not exist since technically the owner can leave almost his whole field to be Peah. See above Tosefta Peah 1:1. Therefore the poor person is never really sure whether the produce left in the field as Peah was meant to be as such and can be taken or it still belongs to the owner, thus requiring the poor person to make sure that it was left for him.
I would like to point out that in the above discussion I was really careful to differentiate between Leket and Peah, but not between Shikcha and Peah. Nowhere in Talmudic literature does it say explicitly if Shikcha needs to be specifically designated as such by the owner like Peah or if it becomes Shikcha automatically when the sheath is forgotten regardless of the owner’s intent. Saul Lieberman in Tosefta Kifshuta (on this Tosefta, note 12) writes that Shikcha is just like Leket and it does not require the owner to proclaim it as such. He does not state a source for this statement. Even though based on the reasoning that I just explained that the minimum and maximum amounts by Shikcha are well defined (only 1 or 2 sheaths, but not 3) I am not so sure that it is completely the same in this aspect as Leket. The reason I am skeptical is because the Mishna Peah 5:7 says that if the workers forgot a sheath in the field, but the owner did not forget it himself then it is not considered to be Shikcha. Talmud Yerushalmi (Peah 5:6, Daf 27b) learns out this law from a verse in the Torah. It also adds that not only the owner must be personally aware that he forgot this sheath, but he also must be present in the field during the harvest when this sheath was forgotten. However if he was not present in the field during the harvest and still he said that the sheaths that his workers forgot in the field should be considered Shikcha, they are not considered to be Shikcha and therefore remain in the owner’s possession. The Yerushalmi learns this particular law from a verse in the Torah as well. All of this implies that Shikcha requires a certain amount of intent from the owner. We can even suggest that since the case of the Mishna where the workers forgot sheaths without the owner’s knowledge is really common, then for sure it would be the responsibility of the poor person to go and find out if the owner intended to leave these particular sheaths in the field, since if he does not do so he may end up inadvertently stealing them, because they are not considered to be Shikcha. However it is definitely not like Leket where the owner does need any intent to leave it at all and it becomes Leket as soon as it falls out of the workers’ hands without any knowledge of the owner.