The pashut pshat why we need 4 cosos is like the gemara says in pesachim (117b): ???????? ?????? ?????????? ???????? ??????? ???????, ???? ??? ????? ???????? ?????? ???????. Meaning, chazal were mesakein to do four mitzvos al hacos on seder night. Kiddush requires a cos, we say the haggadah al hacos, we bentch al hacos, and we say hallel al hacos (cos yeshuos esa uv’sehm Hashem ekra). One can ask why we’re limited to only have 4 mitzvos al hacos, but these are all specific mitzvos that have a shaychus to being said al hacos. We say the hagadah on the matzao (lechem sheonin alav divarim harbeh), so it’s not strange that it must be said on a cos as well. See the haggadah m’beis levi (brisk) where saying the haggada on the matzos is compared to saying kiddush on a cup of wine. The lashon of the Rambam in hilchos chametz u’matza perek 7 is explicit that each of these mitzvos need a cos: ???? ????? ?????? ???????????? ???????? ???????? ???????? ?????? ???????? ???????? ????????. ?????? ???????? ?????? ?????? ???????? ???????. ????? ?????? ?????? ?????? ??? ??????????. ????? ?????????? ???????? ?????? ????????? ?????????. ????? ???????? ??????? ?????? ??? ???????? ?????????? ?????? ????????? ????????. See the Brisker Rov on the rambam perek 7 (in sefer) who explains this aspect of the arba cosos at length.
It is true that chazal darshen in shemos raba (6:4) that the 4 cosos are c’neged the 4 leshonos of geulah, but, as R’ Belsky explains in the haggadah b’tzeis yisroel, this is just a remez of chazal and not at all the ikkur reason for 4 cosos.
The brisker rov (in sefer ibid) also explains that there is another demension of 4 cosos, which is the din shtiyas yayin. See R’ Belsky’s haggada on this as well, that drinking a lot of wine shows cheirus, as the gemara quoted early said ???????? ?????? ?????????? ???????? ??????? ???????.
