And you are also correct - the wealth did come first, then the reserve currency, and the USA has declined since then. Yet my point is true too - you've been sending paper overseas and receiving goods in return, which I see as real wealth. So how do we reconcile these two truths?
I think that the decline in the USA's real wealth is not due to having the world's reserve currency per-se, but rather decadence and apathy. Earlier generations worked hard and build up the wealth of the USA, creating a wealthy country - but one that was inward-focussed. This focus continued up to WW1, and in a waned form up to WW2. In WW2 this vast wealth was converted into military power, projected outwards (contrary to the previous philosophy), and used to achieve a great military victory. After this point the USA essentially ruled the world through soft power projection (other than the Soviet bloc where that power projection did not reach).
This achievement of the pinnacle of power, and the rewards of the massive industrial capacity flowing down to people, raised living standards so high that people no longer felt they had to work as hard. Life was now easy, and the focus of life was improving living standards, not building a sustainable society (it seemed you already had that, so people could now focus on their personal desires). And that began a period of decadence that has bled the power of the USA through a thousand little cuts.
Buying "cheap foreign televisions and microwaves" is wealth. It does improve the standard of living - if you don't have to spend as much to buy a microwave, and don't have to spend as much time in the kitchen "slaving over a hot stove" as a result, the extra time and money can go into other things that you enjoy more also. We look back on the "good old days" but forget how much work they involved and how little leisure time people had. All those cheap gadgets are real wealth.
But they are not the sort of wealth that builds the future of a country for generations. They are the sort of wealth that is enjoyed in the present. It's like buying icecream vs buying a spanner.
So I am correct that the USA has brought in wealth through having the world reserve currency - but you are correct that it is the sort of wealth that ultimately decays rather than builds.