Realistically this is a solved problem and manufacturers have been doing it in similar ways for some time.

Raw files from Canon and Nikon (and probably others too) use a JPEG-Wide variant that is similar to normal JPEG but capable of 16bpc. As it is essentially working on a monochrome image it only has to deal with 1 channel per pixel (and the conversion to RGB is processed later). This is the best place for savings in the workflow as less data in means less data out, plus any compression artefacts will be more likely to show up in the RGB image as a little chroma noise which we tune out quite well.

This means that the problem is not with the OP's correspondent's workflow but with their tooling. Essentially what they've done is bought a sports car and now refuse to drive it fast because of the cost of fuel.

So, if you want to convince them to use raw then you need to show that the value of the extra information in shadows and highlights is worth the extra time/space needed for dealing with the file formats that hold the information. However, if they think the speed is more important to them than ability to work in post then there will be little you can do to change their minds.