>

It really is at least most of them.
Here's a wikipedia page of direct US involvement regime change in Latin American countries.
This doesn't even include the indirect ways we mess with them, like drug cartels legally buying their weapons here or the war on drugs.
Most are fleeing completly lawless countries that are being run by gangs and drug cartels. Others are fleeing cripling poverty. For them its a choice of  Illegaly immigrating into the US seeing your entire family die. If you can solve those two problems and youll drastically reduce illegal immigration . >

It would have helped if the US hadn't intervened in these countries thereby destabilizing them which contributed significantly to the conditions these countries now have. >

So let's be real here as bad as USA was in cold war it's not "these countries" as if all or most it's some.