Every time we go to South America, we rent a car.
But if your visit will only be at Iguasu Falls, a car is probably not the best idea. Car rental will likely cost about US$100/day. When we visited, we drove from São Paulo to the Brazilian falls, only to find that we didn't have papers for crossing the border.
In the falls region, a car will mean unnecessary red tape anytime you cross the border, and it will be expensive. You'd do better taking taxis in this small area. The longest one-way drive you can make is just 30 miles, between the two national parks. Everything else, including airports and the sister cities, is less.
To answer your question, though, in principle it is possible. In our travels, we've crossed the borders many times. Be mindful, though, that there's more red tape, for proper papers, international insurance, and stamps from the border patrol, than you may be used to in North America, and a lot more than in Europe.
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