Even when Israel and South Africa joined the club, nothing really changed. South Africa eventually relinquished their weapons.
Now Pakistan and North Korea have no problem rattling sabres and threatening their neighbors. Iran can't wait to use nukes to destroy Israel. I have no doubt that regimes like these will use nuclear weapons against their neighbors. Additionally they will put those weapons into the hands of surrogates. This will, of course, result in their own destruction.
(And call me cynical but I have a hard time believing that South Africa relinquished all their weapons.)