The FAA removed “declaring an emergency” from the AIM a few years ago but old habits are hard to break. The idea of communications is to get a thought or message to another person. “Mayday Mayday Mayday” means you are declaring an emergency. Saying “we are declaring an emergency” to a FAA air traffic controller who is required to be fluent in English would also get the thought across that they are declaring an emergency.
During a developing situation departing a major US airport, it became obvious that ATC didn’t know what a PAN was so we ended up “declaring an emergency”, which got us assistance straight away. Despite having been brought up on the formality of ICAO standard RT, when you are both native English speakers it can make sense to partly revert to a normal conversation to get details and needs across quickly. It probably won’t work as well in China...