Coverart Issue For Car Audio Player

None.

I would assume that 1 method should be enough: either the player still needs folder.jpg - then it usually does not show the embedded cover or the other way round.

What you could check: does this really only apply to new files?
If you have a file that does not show the cover in the car - could you make a copy of it and then modify the copy so that it displays the cover in the car and see what the differences are?
and then please make another copy of the original file without displayed cover and check it with the recommended file checkers and see if there are any problems.