JOB ... every clearing firm has a 24 hour desk, so, technically every brokerage firm has a 24 trading desk. Some may offer it routinely, some you may have to ask. We must remeber, we have sopfistication in our trading well beyond most. Brokers pretty much assume you're mindless UNLESS you let them know otherwise ... that's what the interview/job description is all about:)
The advantage is being able to place trades live at any time a session is trading. You can accomplish the same thing by having access to most electronic trading platforms ... not all, but most.