Under area-scored rule systems and AGA-like systems filling the ko doesn’t cost you anything, so you may as well. If one of those systems has a local ko rule instead of the AGA’s super-ko rule as cited above, then filling the ko becomes mandatory.
Japanese rules technically don’t allow play to continue to resolve disputes, since under pure territory scoring forcing a capture can change the score. Hence complicated rules like “bent 4 in the corner is dead.”