Sure, but I value human lives much more than animal lives. Our best weapon against malaria causes collateral damage to eagles. It sucks for the eagles, but it's more important to prevent the deaths of millions of humans.
The whole bald eagle or malaria dichotomy is false. Any country that has an actual malaria problem can use DDT to control it, if they think it is effective (however it is becoming less and less effective, because mosquitoes are becoming resistant to it). Some of these countries still use DDT. The US eradicated malaria from our borders by other means long time ago.
In the US the debate about DDT was whether to use it as a pesticide. So the choice was about killing the bald eagles and most of our other birds, or slightly increasing pest control costs for farmers and people with lawns.
It affects other species as well. Also, eagles becoming extinct will have far more consequences than a few fewer birds in the sky. Since they are apex predators, everything below them in the food chain will be affected. And guess what's also part of that chain? Farms and livestock.
Ecosystems are complex enough that we have very little information on all the interactions that could happen. It's more than just a bag of organisms mixed together. A better analogy is the network of files and components loaded up during the boot process. Especially early on, each piece is crucial to what happens next.
Humans are animals. What affects (kills them)animals affects humans(kill you).
We have one weapon way more powerful than DDT. It is called intelligence and knowledge, things like controlling pools of water is way more effective that DDTing everything.
People with lack of intelligence or knowledge wants a magic pill that solves all problems without having to think, but this has an enormous cost. When I eat fish from Ebro Delta I'm eating DDTs thanks to them(they are forbidden but some people continue using them).
I would not rely on our "mass intelligence" to be our savior. The behavior of masses is dominated by factors which are far far away the 'rational' choices and the best interests of whole communities. This is why we always talk about "if only we all did X", and the reason everybody in the pub knows the solutions of big social issues ("the solution is so simple, just do X") is because people assume that we can control ourselves and behave coherently as a group.
Yet people find easier to think of the problem from the other side and think that a bunch powerful people who bend the world to their own interests. It is true, there are those people, their effect is significant, but they are part of the game, they cannot control even themselves and their peers, not even when it would be in their interest (as a group).
Eagles are just the most visible symbol of this degradation of the entire food chain/ecosystem. You start doing something that kills the top or bottom of the food chain, and sure enough, the rest WILL follow, including us.