Sure, so if a Iranian helicopter carrier parked itself in international waters near New York City, everyone would be totally chill with that right?

It would be surrounded and hounded by the Navy, just like the soviet fishing trawlers.

Yes, but it's also Iran. What you're not getting is the "mortal enemy moving a war machine right at your gates" bit.

What you are failing to comprehend is that the United States has a policy of enforcing international naval freedom, and routinely transits international waters near many nations. The US has no issue with any vessel's location in international waters, regardless of what nation.

Would the US have any issue if Iran had more and more powerful vessels than the US Navy, all encircling NYC in international waters?

Not a policy maker but probably still nope. International means international, and America is a part of the international community and these waters are vital for trade. It's not like you can conquer a nation of millions with a couple of ships 12 miles from the coast.