I'm British: I use it quite often. Maybe it's rarer in the US?
"John was late for dinner. They were caught in traffic." is perfectly correct usage (however if you'd just called somebody by a gender-specific name there's not much point in then being gender-neutral).
"John was late for dinner. They were caught in traffic." is perfectly correct usage (however if you'd just called somebody by a gender-specific name there's not much point in then being gender-neutral).