I'm not sure "efficiency" is the right term here. My understanding is that to get "more efficient" execution, you'd have to perform better with the same amount

I'm not sure "efficiency" is the right term here. My understanding is that to get "more efficient" execution, you'd have to perform better with the same amount of resources. But parallelism allows using more resources (particularly CPU cores) for a query, while the overall efficiency (the total number of instructions, CPU time etc.) remains about the same. It's just that it's split over multiple cores. So if all CPU cores are already saturated on your machine (e.g. because you're already running multiple queries), it's not going to improve things.