Drfu,
Trace elements are not what feed corals.
Trace elements provide the minerals necessary for the corals to carry out their life functions.
Simply put, to feed a coral, they require sugar and protein. The zooxanthellae through photosynthesis provide the sugar. For protein, corals need to capture prey and digest it.
SPS corals require much less protein than larger fleshy corals. SPS corals can get by with bacterioplankton which will occur naturally in your aquarium.
Photosynthetic corals with a larger fleshy mass require more protein than that and will benefit from extra feeding.
Non-photosynthetic corals require all their nutrients from capturing prey.
If you try to keep all those corals in the same aquarium, you will end up either underfeeding the larger fleshy corals or overfeeding the smaller SPS corals. Nutrient overload will give you algae problems and suffering corals.
I don't come across much in the way of debate anymore regarding coral feeding other than aquarists trying to fit a square peg into a round hole. They try to force corals to survive in environments that are unsuitable, trying to create a certain look but become discouraged when they run into inevitable excess nutrient problems.
In order to save you some grief down the road, I would suggest that you limit your coral selection to a certain type, learn about the proper care for them and keep those corals only.
There are quite a number of good studies out that will help you learn about coral feeding.