I saw in Tshuvos R’ Akiva Eiger, where they bring down his Takanos for his shul, they write that he paskened not to sing anything before Shmoine Esrei. I don’t know if this precedes him or not.
There is a very simple reason why some Yeshivas don’t sing Kedusha: i heard a mashgiach telling a bochur who davened for the omud not to sing Kedusha, because lots of bochurim who are willing to daven for the omud are too self concious to lead the kehillah in singing, and won’t daven. Therefore they prefer not to make a pressure to sing, so no-one sings.