As much as people like to talk about Argentines having dollars and the government not, I gotta ask who are these people besides those in barrio privados and apartments in Palermo/Recoleta/Puerto Madero, because the people I know live paycheck to paycheck in pesos, and are lucky to have even $500 in dollars for an emergency.
But I digress, if the reason dollarization is so appealing to people is because it's a means to halt inflation, this is obtainable via less drastic means. It's like firebombing your house to deal with cockroaches, sure, it will do the job, but you're gonna have a pile of ashes afterwards.
The prudent and easier thing to do, in my opinion, would be to stop having the BCRA cover fiscal deficits via issuance, maintain a positive interest rate for both deposits and loans above inflation by several basis points, and encourage in-bound tourism/exports to build reserves with the goal of eliminating the cepo.
If you want people to use the banking system instead of their mattresses for dollars you could even pitch something like an FDIC scheme backed by a non-Argentine institution such as the AIIB/BRICS Bank to encourage the entry of dollars in to the formal economy via deposits.
I get people want to kill inflation, but dollarization is a double edged sword, and I'm saying this as someone who would benefit personally from dollarization.
Finally, as to comparisons of monetary issuance with the US, let's remember the dollar is the global reserve currency unlike the peso, which means the US can print dollars without many of the issues other countries would face when doing the same because there is inherent value associated with dollars. I'm not saying this will last forever or is fair (and we're seeing increasing numbers of currency swaps by countries) but people will take dollars either for payment or will exchange them for the local currency everywhere, while people in Argentina don't even want pesos, forget neighboring countries or the US.