You're right about the age of the term but it's nothing to do with combat, but rather just a nice sounding umbrella term that makes talking about joint forces easier because every military service has their own special name for their personnel (soldiers, sailors, Marines, etc..).

The POGiest of POGs are "warfighters" and individual organizations within the DoD proudly advertise how they serve runny eggs and chicken to warfighters every day or issue their uniforms/equipment with incredible lethargy or maintain their personnel records in 20+ different systems duct taped together.

"Service member" does get used a lot still. Usually abbreviated to "SM".

Source: Personal experience in both combat arms and non combat arms roles.