Arguably it's the threat of nuclear annihilation that's done that.

If anything the aircraft carriers are what the US does to stir up shit around the globe: Korea, Vietnam, Nicaragua, Panama, Grenada, Iraq, and Afghanistan among others.

It's not just the nukes. What makes arms races start is a relative parity of force. If you have one carrier and the US has eleven, there's no point in building another one or two without building ten. So you either bite the bullet and build ten, or you don't build any. That's a whole lot of money to shell out, so most countries won't do it.

But let's say you have a carrier and nobody else has more than one. Building a second makes you top dog and opens up a range of strategic options.

That's amongst the superpowers. And even then, "everyone" knows that Nukes are last resort. Carriers allow constant ACTUAL power projection that can respond to events that don't require nukes.