The poor quality of the video that the BBC is streaming is really caused by the sampling rate. They are choosing to stream a video content that has a low sampling rate. It is not the fault of the mpeg-4 streaming system. You can stream video at TV broadcast quality using mpeg-4 so it is just a policy decision of the BBC.
FBT streaming system produces a tiny viewing area with poor quality and there is not much to be be done about it. It has nothing to do with the sampling rate, just the technology involved causes it.