It occurs to me, and I have not seen it mentioned so far, to ask, immediately after a sudden depressurisation, in what state are people's ears? Are they capable of hearing an announcement? And would a partially understood or misunderstood PA actually increase the chance of panic compared with no announcement? Leaving the PA until everything has levelled out seems sensible to me.
A warning about the rapid descent should be given in the safety briefing, however.