Hartington
There is much more to BA's network connections to South America than via Madrid with Iberia (in addition to the directly served routes of GRU, GIG and EZE).
That is what alliances are all about - providing links through partners where there is not the demand or the capacity (LHR - where the resources/slots have to be deployed as profitably as possible).
BA connect to SA destinations using alliance partners AA, Lan and IB through their own destinations and those in DFW, MIA, EWR, MAD etc etc.
I'm sure I haven't covered all the options, I suggest a little research through the BA & One World websites might calm you down a bit.
As and when UK plc have a 4 runway airport to serve our interests then you may well see more direct city pairings. As an example, BA only pulled out of CCS/BOG some years ago because they could redeploy the aircraft more profitably elsewhere, not because the route was losing money.
Morale of the story - don't blame BA - blame the government!