I can tell you right now, the vast majority of Americans do not think about money in this way. They are not using the American dollar because it's "safe" but because it's convenient and easy. And that's not even to say they're lazy, needing to transfer money to buy groceries is expensive. And you may be thinking that you mean retirement funds and savings, not everyday money. Ava, viewing it like that is extremely out of touch with the average American. Most Americans are living paycheck to paycheck. It's why you may hear many poor rural folks talk about gas prices the way you hear upper middle class folks and the media talk about stock prices.
All that to say, I think they trust it, but I also don't think they're thinking about it from that perspective. I don't think many Americans have the luxury of thinking about it from that perspective.
Even me personally, the money I have in retirement savings is in stocks. I'll move some to bonds as I age. I have some money in a savings account that has a nice interest rate but that's really more of a buffer for my checking account. I only recently got a credit card so the idea of using credit more aggressively for short comings like some of my peers do is still a little nerve wracking, but regardless, it's not something I'd even consider having in a different currency because I need quicker access to it.