You're on the right track.
In a normal, non-reserve-currency situation, the demand for a country's currency is proportional to the demand for its products. After all, that's what you use a currency for: to buy the products that are sold in that currency. This has a well-behaved equilibrium, because if a country produces a lot of good products, that means the value of its currency will rise, which makes goods developed in that country relatively more expensive, which cuts demand, until everything equilibrates at a point which is roughly reflective of the actual quality and productivity of the country.
In a reserve-currency situation, the currency is used for many things other than buying the products of the country. For example, oil is priced in dollars; if India wants to buy oil from Saudi Arabia, it needs dollars to make the transaction, and then Saudi Arabia has an excess of dollars. Frequently it uses these to buy U.S. T-bills or invest in American tech startups like Uber or WeWork, both other sources of demand for dollars. The dollar is basically the currency of the global financial system: instead of directly converting rupee to riyal, you convert rupee to dollars, handle your transaction, and then convert dollars to riyal.
This creates a large source of demand for dollars outside of the traditional market for a national currency. Indeed, America's export here is basically financial services, which as a sector has been doing great since 1990, one of the few areas where you're likely to get paid handsomely. The other area is tech, which at its core is about enabling these cross-border commerce flows - Amazon, Google, Facebook, UpWork, Stripe, CoinBase, Ripple, Stellar, PayPal, E-bay, Shopify, AirBnB are all about creating global marketplaces where you can buy anything from anywhere.
Finance and tech crowd out everthing else that you would normally use dollars for. Basically America has specialized in being the global marketplace - it's only purpose is to be the common standard that every other country needs to transact in. Because there's so much demand for dollars simply to do international transactions, it pushes the price of the dollar up. This makes everybody who's trying to sell actual things in dollars (rather than take a commission when other people sell things in dollars) uncompetitive.
It works great, until the rest of the world decides that it wants to cut out the middleman. At that point, since we don't produce anything anymore, we're screwed. America's basically given itself Dutch Disease, where our only viable industry is financial services.