Why do ion leak channels exist?
Check the parameters that go into the Goldman equation... it shows that permeability of ions is as important as their concentrations. If the permeability is zero, there is no potential. Because other conductances are mostly closed at rest, the leak channels are almost entirely responsible for the resting membrane potential (there is a minor component, a couple mV, supplied by the sodium-potassium pump itself, that is missed by the Goldman equation). If there were no leak channels, there would be effectively no resting potential, and certainly no useful one.
Additionally, there would be no return to &quot;baseline&quot; after a signalling event.
Leak channels are entirely integral to nervous system functioning (and the function of other excitable cells, including muscles and immune cells) - a system without them would be nothing at all like what we actually observe in any biological nervous system. The membrane potential massively amplifies the concentration differences into an electrical signal, such that large changes in voltage occur merely by opening and closing channels: very few ions need to move for this to happen, making a very efficient signalling system, requiring only the maintenance of ion concentration gradients (which change very slowly).
I would say it's correct to say that the role of leak channels is quite diminished during an action potential, since voltage-gated conductances ultimately overwhelm the leak conductance. You can see this from the Goldman equation, too. But they are quite important in setting threshold itself, and in returning to rest after an action potential. However, even during an action potential there is very little actual ion flux. Electrical forces are very strong, so not many ions need to move (see again the answer I linked above).