"Should the POC term be discarded in favor of something like "non-whites""
Yes, which is why I use "non-white" all the time, but "POC" only reluctantly when someone else has used it first, and even then try to convert it to "non-white" when an opportunity arises.
POC is a stupid name as it implies "whites" somehow lack "colour" which is obviously untrue. At worst it reinforces the gaslighting that "whites" actually have white skin, something which far too many people still believe despite seeing otherwise with their own eyes every day.
"White" Carlson's skin colour is obviously more distant from optical white than "non-white" Omar's and Duckworth's skin colours.
"Non-white" Navarro vs "white" Thiessen - same phenomenon as above.
"Non-white" AOC vs "white" Yoho - same phenomenon again.
That something like this even needs to be explicitly pointed out is a sign of how psychologically powerful Eurocentrism is. But pointing it out is the start of pushing back.
Bonus video: