A small add-on:

Usually, plants get most their nutrients from the soil, most importantly nitrogen (but also P, K and some others).

In some locations, such as swamps or very sandy soils, there is not a lot of nutrients for the plants to get and these “nutrient-poor” soils are usually those where carnivorous plants live. They simply get the nutrients from insects, which consist of yummy proteins made of nitrogen.

So basically one should not really wonder why carnivorous plants need sunlight. They do photosynthesis by taking up CO2 from the air and using energy from the sunlight in order to produce C6H12O6, Glucose. And I guess this is also what the japanese orchid steals from the fungi - sugar.

Of course these processes do not work completely independent from each other. But Glucose, the product of photosynthesis, is not really considered a nutrient, that would be carbon.