o.O did I read right you are complaining about high CPU usage?
It's a multithreaded engine that can use up to 4 cores effectively and a few extra less effectively. It will max out a quad core CPU if it has the resources and speed to do so.
Video editing and streaming at the same time, then you are probably going to need more cores and dedicated one or two to the streaming audio and video. A Hyperthreading enabled CPU would be prefereable for video work so an i7 3770K would probably be a better solution. Even better would be a hex core CPU so you can use the two extra physical cores to offload the Video Streaming while still having the optimum 4 physical cores for BF4. The Video stream could probably use HT as well giving it 2 physical and 2 virtual cores leaving the other 4 virtual unused (HT is never used in games).
BTW High CPU usage combined with High GPU usage with good frames and no stuttering is a sign of good optimisation as it's getting the maximum from the resources. If you are having low CPU usage with High GPU usage then your GPU is a bottleneck, vice versa and the CPU is a bottleneck. The only time when High usage of a component is considered unoptimised is when the the game is running poorly despite the component being well within spec and there is no external factor causing the problem.
Streaming video is an external factor causing a problem...
PC:
Win 8.1
Intel 3930K @ 4.25GHz
16GB Corsair RAM @ 2000MHz
Radeon 6950 @ 840/1350 (Soon to be R9 290)
Intel 520 SSD
