Probably best to distinguish between processing-heavy and throughput-heavy; apart from the GPU, all those are throughput-heavy but do very little to the data, and I think would not normally have a recognisable processor or an OS. There's the additional problem that they're required to boot, so nowhere convenient to load the OS from unless you scatter SPI flash across the board.

GPUs on the other hand have a full task-switching operating system.

I would be surprised if the faster bus and memory controllers had it (because of latency problems). I would expect something like it on a USB controller, GPU, network or disk interface. I really have no idea what to expect from a DMA controller.