If the aircraft has been operating IFR there is no possibility of confusion as it can only have one type of SAR. While it may not be quite standard there is no risk.
If comms are crap or I'm busy then the brief warning transmission can be a time saver, not waster as I don't have to get you to say it all again. I'm not just sitting there waiting for your call, believe me. Might be the case at a towered aerodrome where they can see you getting ready but not for the rest.
Far more time is wasted by pilots not listening before they transmit.