Testing my (US-centric) understanding here. But I'll argue that the US does suffer for global dollar dominance in that there is necessarily a US trade deficit whose primary results are the exporting of US manufacturing overseas and the creation of the productivity-wage gap that started in the 1970s.
Being the main reserve currency (global reserves are ~60% USD, ~30% Euro and 9% GBP/JPY/CAD) also means local financial crises lead to dollar buying which then affects the price of USD and thus US imports and exports. This is in part why the US has had a policy of discouraging the USD's status as the sole reserve currency - global reserves used to be 80% or more USD.
Interesting! Would it be fair to say that on one hand the US is incentivized to have the US dollar maintain its role as the main reserve currency because it enables access to lower lending rates, but on the other hand too much dollar dominance exposes the US to greater risk?
No, the US gets low rates because of the stability and strength of its economy i.e. both reserve currency use and low interest rates are effects, not causes.
tl;dr: If you want to "own" the financial system, you need to be willing to be an importer of last resort, follow the rule of law, have deep financial markets, a freely exchangable currency, and freely tradeable debt. You also have to be willing to accept either rising debt or unemployment.
These can cause pain to countries who have them. Here's a quote from the piece:
"The one thing both sides agreed on, however, was that the US enjoyed an advantage because of the reserve currency status of the US dollar, with some people even assuming that the US was somehow repressing the ability of Europe, China and Japan to gain the advantage for themselves. No matter how many times the US engaged in policies that tried to shift the benefits to those countries, or these countries engaged in policies that prevented them from receiving the benefits, it was somehow clear to both sides that reserve currency status is a wonderful thing that everyone wants but only the US is allowed to have." (Emphasis mine.)
The status of the USD has also been called the "exorbitant privilege" in part because times of crisis lead to a strong USD and hurts US companies - even when the crisis is entirely unrelated to the US. US policy for well over a decade now has been to encourage other reserve currencies to reduce this exposure.