I am a permanent resident without an Argentine license. I've had a car here for 3 years and never had problems. Based on a previous post here about insurance denials, I contacted my company (La Segunda), and they confirmed in writing that they do not require an Argentine license for coverage or for claims. (Other companies may have other policies.)
The only problem I've had with the authorities was in a routine check in Puerto Madero, where the Prefectura agents didn't like my NY driver's license. I explained that in previous controls in town, the Comisería had accepted my US license without question, and they replied "No, you don't need to have an Argentine driver's license to drive here. But you should have at least an International License if you're going to drive your own car here without an Argentine license." I apologized and promised to get one.
Apparently, the international license is taken seriously here - it's something issued by the police. In the US, it's a nuisance document that the auto club sells for a few dollars a year. So I ordered one from the AAA, which arrived a few weeks later. I carry it in the glove compartment of the car. It's been requested only once since, again by the Prefectura when I was in Puerto Madero. The Comisaría always accepts my NY license during routine checks, of which there have been many. Come to think of it, my AAA license has probably expired - I think they're good for only one year.
I had a minor accident in December and filed a claim with La Segunda. They wanted to see all documents, including my license, and I presented only my NY driver's license. That was sufficient, and they paid the claim.
That said, the attorneys who worked with me to get my resident's visa some years ago told me that the law required me to get an Argentine license if I intended to drive here. At the time I didn't have a car, and I didn't follow through. I subsequently checked and found it to be a nuisance involving an appointment to go at an early hour to some remote corner of the city surrounded by villas. And I never got around to doing it.
Aside from the nuisance, the only issue I know of for expats is that licenses are issued only for the term of residence. So a temp resident needs to renew the Argentine driver's license annually along with the DNI until s/he achieves permanent status.
I look forward to Sleuth's post because I really should legitimize my license. I'm not recommending that others don't do the same - just describing my experiences.