Sharpening itself, is a bit of an illusion. What is does is to increse the contrast between light and dark areas, an effect most prevalent on edges. It is just that the brain interprets this as extra contrast and makes it simply "look" sharper.
Your radio analogy is a good one, but consider this. If you put an amp in nearer the radio on a lossy or long lead, then it will amplify not only signal, but noise too. If you put the amp in a little earlier, then the signal to noise ratio would be better. TV boosters are a great example. They are often put in to amplify the already compromised signal from a poor aerial and you get noise visible on screen. This is what happens in post processing with pictures. If you can get the purest "signal" and then sharpen that, you will get far better results than if you were to try to sharpen the lot, with existing noise and artefacts also being sharpened. This is why you should stick to noise first, sharpening last.
When it comes to being "lossy" nothing can beat a JPG, which is a major reason that many prefer RAW and also that the latter will give you so much more elbow room in post processing. You are not only the photographer with RAW, but also the lab and printing house too.
Conan