Is the US suffering an exorbitant burden? Due to the dominant role of the dollar, the US is able to borrow cheaply from the rest of the world, an effect known as the exorbitant privilege ( https://berkeley.app.box.com/s/oqtzizo8wch5snic1nys7ig01n6f65la). But, as argued by @michaelxpettis, cheap access to foreign credit

might be more of a burden than a privilege. First, capital inflows can depress demand by putting upward pressure on the exchange rate ( https://scholar.harvard.edu/files/farhi/files/glob_imbalances_011620_pog.pdf, https://www.aeaweb.org/articles?id=10.1257/aer.20180608), fostering debt accumulation by low-income households ( https://scholar.harvard.edu/straub/publications/indebted-demand), and leading to

excess capital accumulation ( https://fgeerolf.com/hansen.pdf ). The exorbitant burden might thus manifest itself with weak demand and Keynesian unemployment.

Low productivity growth is a second potential source of burden. In fact, capital inflows might discourage investment in innovation by depressing economic activity in tradable sectors ( http://www.crei.cat/wp-content/uploads/2020/07/GFRC.pdf) and lowering competition ( https://scholar.princeton.edu/sites/default/files/ernestliu/files/liumiansufi_productivity_06122019_updated.pdf).

Third, capital inflows might create financial instability by fostering debt accumulation by households ( https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2655804) and opening the door to bubbles ( http://www.crei.cat/wp-content/uploads/users/pages/EGB_pub.pdf).

An interesting aspect is that policy interventions can mitigate the three sources of burden mentioned above. Expansionary monetary and fiscal policy can stimulate demand, innovation policies can revive productivity growth, macroprudential policies can reduce financial instability

Hence implementing the right policy framework might be the key determinant of whether issuing the dominant currency is a privilege or a burden. This might explain why some countries, e.g. Germany, have been reluctant to encourage the international use of their currencies.

So is the US gaining or losing from the hegemonic role of the dollar in the international monetary system? Lots of interesting research to be done to answer this crucial question!