jimmywanger wrote a good comment, but I kinda wanted to expand on it.

In a certain way, it is illogical. There are drawbacks to adopting a foreign currency. You have to have enough trade with the other country to bring in the (in this case) dollars. You lose the ability to cover short-term debts by printing some money that you can take out of circulation a little latter (no harm, no foul). You also lose the ability for benefitting from seigniorage (by printing small amounts of money, you can prevent deflation as the economy expands and increase government purchasing power). By adopting the foreign currency, the foreign government keeps the seigniorage benefits.

But when your government is so corrupt that it can't be trusted to manage a stable currency, it can make a lot of sense. Right now, Venezuelans have no reasonable way to conduct commerce. Bolivars lose value so quickly that you never want to invest in enterprises or hold cash. If I have $100 on Jan 1, it's likely worth at least $95 in purchasing power on Dec 31. People expect inflation in Venezuela to be 1,600% next year meaning that $100 on Jan 1 would become $6.25 in purchasing power on Dec 31. People would rather hoard goods than cash - even goods that Americans would see as losing value quite quickly. Cars lose so much value when you drive them off the lot (the adage goes), but that's way better than the amount of value lost in Venezuelan currency over the course of a year. Currency should lose value slower than quickly depreciating goods.

When you don't have a stable currency, it's hard to operate economically. In many ways, if you have a good to sell, you don't really want to exchange it for cash until there's something else you want to buy. If there's a week delay between you selling what you own and then you buying the new thing you want, you've lost a lot.

By adopting a stable currency like the USD, it would allow them to have a functional economy where people could buy and sell goods and invest in things and make logical choices knowing that the currency has a stable value - rather than running around hoping not to be stuck with notes that are going down in value faster than any good.

When your country is so corrupt and incompetent that no one will trust your leaders for many decades to come, it then starts to make sense to adopt a foreign currency. The people then see that they can rely on the currency because the competent US government is in charge of it - and for all we might complain about the US government, it is competent by global and historical standards. It gives people a stable currency that the Venezuelan government can't offer them.

Venezuela wouldn't answer to the Fed or get to print notes. They'd just be exporting things like oil to the US, getting USD in return, and then using that USD locally as a stable currency.

Someone else mentioned Brazil. Brazil is one of the few places to really combat hyperinflation. The thing is that it's hard. You can't just say, "we're going to be good starting now. . .trust us". People don't trust you yet. It takes years for people to trust that you won't fuck up a currency after years of having the reputation of fucking up currencies. Let's say that Venezuela stops printing money today and acts like a good government. Hyperinflation continues because people don't truly know they have stopped printing money and don't believe the government when it says it has. So when the government needs to pay for goods and services, it suddenly faces very high prices without the printed money to pay for it. Most likely, the inflation will break the government's plan of not printing money since they would have to shut down the government due to lack of funds faster than people would trust that the government had stopped printing money.

Brazil overcame the issue by running two simultaneous currencies - one real paper currency that kept inflating and another non-paper currency called the "real" with stable prices. Stores had to denominate their goods in terms of the new "reals" and each day an exchange rate between the paper currency and the "reals" would be published. So, bread would always be, say, 5 reals, but on monday that might be 10 of the paper currency and on friday 11 of the paper currency. Eventually, people trusted that the "real" was stable, the government took the old paper currency out of circulation in exchange for new paper "reals" and people continued to trust it.

But it's hard to fight hyperinflation because when you can't measure and guarantee government actions, it's about trust. Trust is something hard to regain after decades of reasons not to trust.