I make chips that do both. Image compression, which is completely different from data compression, requires a lot of memory accesses, both for synchronization and buffering, which is what consumes most power in a chip. Or, if we count the number of gates, they're in a completely different ballpark.
Post-processing of that nature is usually a very straightforward pipeline in hardware that only involves local operations (often mults and adds, sometimes a LUT) which can be performed on the pixels as they stream by. In comparison, compression is very efficient, too, but the paths are more complicated and involve many different operations that have different timings. You need to do the debayering, convert the spatial pixels into frequency data (wavelets), perform an analysis for the compression and sort out what has to be left out while maximizing the quality (that one is very limiting!), quantize the data, perform arithmetic encoding, and format the stream output. It's quite hard to balance the lengths of all parts of the pipeline to preserve the top performance while not using too much memory, especially at high quality compression rates (the ones used in the HE modes) because they output quite a bunch of data whose size can vary wildly from one area to the next. It's a problem common to all compression algorithms I've seen.
But I don't know exactly what they're doing in their post-processing. It's true that their demosaicing - Nikon's demosaicing used for the post-processing and JPEG compression - is very good, so it must be more complex than just applying a simple interpolation.
Those operations are performed
in a separate pipeline in their chip, so as you said, there's no apriori reason not to provide the choice in precapture. Except, as
@JAJohnson clarified, pre-release capture
is only available for 30/60/120 FPS modes, which can't be achieved in lossy raw compression because of the reasons given above.
So it's a problem of raw performance (pun intended), not a problem of CPU/ISP overhead. We could, theoretically, get a pre-release capture mode at 20 FPS if it were available for other modes than high-speed capture, but for some reason, it's not. Maybe Nikon decided the odds of getting a good pre-capture shot at that framerate wasn't worth the trouble? I don't know.