Considering that hunters shoot millions of lead bullets each year, it seems a small problem? It's suggested that birds eat guts from eviscerated animals that hunters leave behind. Perhaps a policy of burying or scattering the guts would solve the problem?
Here in Northern California, we're actually unable to use poisons on pest rodents like squirrels and rats since they often enter the ecosystem through raptors ingesting them.
My friends with a lot of land were advised to get pellet guns and air rifles to deal with their squirrel problems. It's considered the lowest impact to the ecosystem and food chain.
"Bald eagles across the United States are dying from lead poisoning":
https://edition.cnn.com/2020/02/16/us/bald-eagles-dying-lead...
"CALIFORNIA'S LEAD AMMO BAN IN EFFECT JULY 1[2019]":
https://www.gohunt.com/read/news/californias-lead-ammo-ban-i...
I think most of this is anti-gun lobbying. When people are reduced to stoning wild ducks and spearing deer then anti-gunners will ask Congress to ban sticks and stones.
You shoot steel from the same barrel as lead, it's a quite different effect. Range, drop, spread are all different, and lesser.