Why are lens and body caps opaque instead of transparent?

No! You want opaque lens caps because:

1. Keep light out of the camera when not using it. In film cameras, the sensor is effectively always on. The shutter should in theory block all light, but stuff happens.

   With digital sensors, light hitting the sensor when not exposing doesn't corrupt the next picture, but you still want light not entering the lens when it doesn't need to. With the lens cap off or transparent, you always have to think about accidentally pointing the camera at the sun. Highly concentrated sunlight for multiple seconds can cause damage to a camera.

2. Various things degrade with exposure to UV. It's best to block this as early on and as much as possible, like when the camera is not in use.

3. Most cheap plastics that would be used for such a lens cap would themselves be susceptible to UV. That would cause them to yellow, crack, become weak, etc.

4. It doesn't solve anything. You never explained why you think light entering the camera helps reduce fungus growth. Perhaps you are thinking UV from sunlight will inhbit it. That is probably true for the fungus, but this "transparent" lens cap will probably absorb significant UV. If not, the lens coatings and the glass in the lens will absorb it. There is little UV left deep in a lens.

   Even if the fungus were killed by UV, other organisms will benefit from the extra light.