Holding the printing presses of the worlds reserve currency is a clear short term advantage for the US.
The inflationary implications of monetary expansion are diluted due to foreign held dollars.
For example if there were no foreign held dollars and you print up new currency equivalent to say 10% of all the money in the country then you will expect, all other things being equal, to have an eventual 10% rise in prices.
And what has just happened is that the government, or whoever had the keys to the printing press, has stolen 10% of the country's wealth. Citizens may or may not complain, they may accept this form of taxation or not. They would be wise not to as the detrimental impact of the disincentive to save is taken on without compensation.
If however there are a great deal of foreign held dollars, say 50% are foreign held. Then when you print up new currency equivalent to 10% of all the money in the country, you will have only a 5% rise in prices.
Half the burden of the taxation has been carried by the foreign owners of the dollars. Your citizens will no doubt be delighted by the reduced burden and accept the inflation. The disincentive to save has been reasonably compensated.
However how long will the foreigners wear it?
And if they decide to get a new reserve currency what will be the implcations of all those foreign dollars coming home?