Here's my take on this....
The ecosystem has an artificially inflated food base from crop cultivation.
If the farmers suffer enough losses from crop depredation, they'll stop growing crops. Then all the birds and quite a few people starve.
Shooting ( not hunting) the birds keeps the system profitable.
While it's not everyones' cup of tea, organized shooting parties serve a need and fuel the local economy in a Third World country.
The dead birds get eaten.
I'll never be able to afford Argentina. If I could, I might do as a buddy does and limit myself to a flat of shells in the AM, another in the PM.
I would probably work on certain angles and presentations rather than the biggest body count, but that's just me.
My recommendation for anyone going to an Estancia is to stop when it starts feeling like work.....