Well, sure, but that hostility does not exist in a vacuum. Leftwing governments south of the US are pretty hostile to the US, in large part as a consequence of US intervention in those places a few decades back (not militarily of course because, well, it'd be pathetic and pointless). As has been the case for the past decade leftwing governments in south of the US would rather sell their souls and children to china and russia than work alongside the US. Which is why countries south of the US have acquired massive debt at loan shark rates from china.
TBH I am skeptic that the US intervened in Bolivia recently. It is true that the right wing government they had while evo was not around was comically corrupt though. Unfortunately due to the US's interventions back in the day this is an easy boogieman for the left wing parties here to exploit...
I don't think the issue here is "learning to stabilize" anything. How would that even work? Normal diplomatic and economic relations are just that, normal. And it would come a long way towards actually competing with china's agenda in this part of the world (which includes the aforementioned massive loans, investments and chinese companies buying everything). The EU should also have an interest in furthering these normal economic relations more to compete with china's agenda for that matter. That is not to say there isn't stuff happening in these regard but to me it always felt like the US and EU should be doing more because china is absurdly aggressive.
What I mean goes beyond investment (and of course, the EU should also be present in these things, but i see the EU more responsible for northern africa and the middle east than south america).
I think the US needs to undertake an honest push here to build up trust and soft power in that region again. I do not think the US intervened in Bolivia, but it also surely did not put effort into masking that it was kinda fine with the right wing takeover. I am not a huge fan of morales and his claim that the rightwing takeover was orchestrated by the US is bullshit, but it cannot be overlooked that bolivia under Morales is a somewhat stable country for the most part and extreme poverty declined.
There is room to become a positive force in the development of souther america, with a huge focus on two points, fighting poverty and fighting climate change.
Both the US and EU should invest considerable effort into making their 'backyard' ready to stand on their own two feet in a world in which resources will be much scarcer than now and many places will not be habitable anymore (especially in the middle east and south america).
If they do not do that, they are going to look at chaos at their borders that dwarves anything they saw before.
Afghanistan shows us (and lybia shows us and yemen shows us and...) that once a state failed, it is insanely hard if not impossible to rebuild it. You can pacify it for some time, but at the end of the day, without the foundation for a flourishing state, you cannot stop the decline.
The EU will look at a neighbourhood with more and more states that might fail, like lebanon or morrocco, or egypt.
But the US has their own risk factors down there and right now there is still time to minimize that risk. In 20 years, countries that are somewhat stable now might become half a dozen of Venezuelas.
