As I understand it, the default function meant that one touch per stick imitates touching a finger on a touchpad. This touch is simulated as long as the gamepad stick is constantly pressed. Is it possible to make a single tap on a stick to activate the touch mode and not require a constant tap on the gamepad stick, then it would be possible for the gamepad stick to rotate freely in all directions. Pressing again would disable touchpad mode. Alternatively, other combinations can be envisaged.
As I said before, pressing and rotating the sticks at the same time causes certain difficulties.