It would not be normal in a few years. The US is also a very large manufacturer, much of which is in more "essential" goods such as large equipment. Individuals and governments across the world hold US treasuries, so the US disappearing would wipe out trillions of dollars of assets. The US currency is a common reserve currency across the world, and would become worthless, creating a massive domino effect in banking across the world. Many important internet services would no longer function. Countries like Japan and Israel which rely on the US for defense would suddenly face a decrease quality of life and even existential threats. The countries which rely on US aid would suffer greatly.

Is the world dependent on the US? No, you're right that dependent is a very strong word. However, the US, for better or worse, provides a very high amount of global stability. The US has a massive economy and a very strong military, and the world would be very different if any country like that were to fail.