The sparse Fourier transform is also probably not useful for any of that stuff, because accurate results are needed (not just getting one or two of the main tones). Transforms are not the bottleneck at all in video encoding, and even in audio encoding, split-radix FFTs and the like are very fast.

High-res Dirac video encoding is definitely possible in real-time, you just need a very optimized encoder, which doesn't really exist. Dirac's main speed cost comes from the overlapped-block motion compensation, not the transform.