assuming that a mitzvah asei needs to be derech achila, has anyone raised the issue how the matza that ashkenazim eat and the way we gulp down the kazait is shelo k'derech achila?
Simcha Cohen
Yes this question has been asked. The Gemara on 115b quotes Rava who says that one who swallows his Matza has fulfilled the Mitzva. The Toras Chaim( Chulin 120) proves from this that one fulfills the Mitzvah even if one did not derive benefit from it, since Mitzvos were not given for benefit and therefore the concept of eating does not require benefit. The Toras Chayim explains according to this why the Gemara requires a pasuk (lechem oni) to explain why dissolving the Matza and eating it does not fulfill the Mitzvah even though this is not actually "eating", since one is not required to eat and derive benefit.
According to this there should be no issue with gulping down the Kzeisim. However Mishne Le'Melech (Yesodei Hatorah 5:8) disagrees and says that just as in Issurim of Achilah if one derives benefit in an irregular manner one is exempt, with Mitzvos too if one eats in an irregular manner one is not yotze. The Nodah B'Yehuda (Yoreh Deah 1:35)concurs and quotes Mishne Lemelech that the reason that swallowing Matza is Achila is because the Matza itself is not intrinsically inedible (i.e. bitter or exceedingly hot) and therefore even though he swallowed it it is Derech Achila. According to this view as well if we gulp down the Kezayis since the Matza itself is edible this constitutes Achila according to Mishne Lemelech.
Yoel Domb