Most Venezuelans are employed "en negro"- their employers don't pay taxes and therefore they do not contribute to support local hospitals.
Therefore, I have no "need to find other nationalities to beat up on", as you so kindly put it.
I'm not sure what employment "en negro" has to do with the topic, I believe a huge number of Argentinians do the same (and it should have been a priority for the current government to shut this down, but I guess culture wars are more exciting).
My point is that any new rules are very unlikely to make your cleaning lady any happier, the Venezuelans are mostly documented, residents or citizens, as a quick AI check reveals:
"Argentina hosts a smaller total volume of Venezuelan migrants compared to neighboring heavyweights like Colombia, Peru, or Chile, but stands out for offering a higher rate of formal legal residency, a remarkably high concentration of university-educated professionals, and arriving predominantly by air rather than overland".
The Venezuelans who made it this far were relatively ("relatively" is doing some heavy lifting here) well off, as a plane ticket cost around USD 1000, and even a 7 day bus trip (when that was possible) cost USD 500. That, plus a reserve to cover the costs of the first few months here. Most of them would have come with the necessary documents to immediately apply for temporary residency, by Mercosur rules, 2 years of that and then permanent, and then apply for citizenship.
Also from AI: "While countries like Colombia host over 2.5 million Venezuelans and nations like Peru and Chile host upwards of 600,000 to 700,000, Argentina accounts for a more modest population of roughly 175,000 to 200,000 registered Venezuelan residents". so I think "overrun" is probably an exaggeration. Mind you, they can be a noisy, extrovert, lot.
Again, about employment "en negro" and not paying taxes, a lot of Venezuelan immigrants are delivery workers for companies like Rappi, or PedidosYa, or work as Uber drivers. Maybe I'm naive, but I would expect those companies to insist on their workers registering as Monotributistas with ARCA (as well as having insurance, and so on).