The MD80 'wedge' fairing was known as the 'screwdriver' and was developed in the mid-1980s. It was an easy retrofit. American Airlines later obtained an STC for their own design of fairing which was cheaper than the official MDC part.
I don't know why Boeing reverted to the conical fairing on the 787 but the 777 has a very noisy APU on the ground on account of a very short jetpipe, due to the shape of the fairing it exhausts to the side.
https://www.youtube.com/watch?v=qc_nFCHnr78
Perhaps the longer axial jetpipe in a conical fairing is quieter.