But are there studies that show that trace elements are NOT essential? Or is this just an area that hasn't been researched?
I would guess that this is true of all trace elements at some concentration. That doesn't mean that the same trace elements aren't needed at lower concentrations.
Skepticism is certainly warranted here. And it's hard to argue with your success, Dong - you have beautiful tanks with gorgeous corals. But, if I'm correct, you do add trace elements in that you do water changes. My theory (and that of many others) is that water changes are an inefficient way to add trace elements - why not just add them directly? Yes, there's a chance of overdosing them but by correlating the dosages of trace elements to calcium consumption, many folks seem to be having great success. That's how the ATI Essentials and the Red Sea ABCD systems work.