You cannot sustain the price of a currency by printing more.
Who has the usd to buy the coin back when market actors want to sell?
Whoever holds the backing of the currency is the single point of failure.
You can hold a peg just by controlling the printing process as long as you're likely to have to print in future. As long as that's true, you can incentivize people to destroy coins when the value is too low by giving them vouchers to allow them to print in future when it's too high. These could just be a special kind of transaction on the blockchain that anyone could make, so as long as you have a way for the network to know the exchange rate it's pegging to you don't need any central authority controlling printing or destroying coins.
This isn't a sure thing if you get a lot of demand coming in and you print a lot of money to meet it, then it all goes away and everyone decides your currency is rubbish. But if you're pegging to a regular fiat currency the hurdle you have to clear isn't very high; You don't even have to keep demand steady, because the coinage you're pegging to is gradually getting debased.
