I understand what you mean, and yes you are right the world suspect the possibility of "A bomb". No one had figured out until United States figured it all out. After done dropped two A bombs, Spy vs Spy started right away. So, think this way, if US never dropped one but tested, passed and kept secret then it would be our best defense mechanism against other countries, plus once other countries tested, United States WILL know and spy on them and make sure they aren't stupid enough to drop one.
Your right about us being only country to nuke, that is because nobody else has it. Today, technically too many people has it. Think about this, once one country decided to nuke, how many other countries is gonna to be pissed off and follow? Hence domino effect.
Its just same as it takes one to start fight that leads to the riot.