There been a few very good answers to this statement, but Ill add one.
Having to 'prove' you dont, and wont cause harm in future, is a fallacy, its like saying you cant have a driving licence unless you can prove youll never cause an accident, or be issued an FAC/SGC unless you can prove you wont shoot a person.
The amount of harm spent lead projectiles has caused is not a measurable thing, its a loose estimate, likely over exaggerated (due to the bodies compiling the data) but is a useful weapon in demonising shooters.
If the WHO, REACH GOVUK ect really wanted us to stop using lead they wouldnt need to ban it, but they have anyway, but you could simply slap a tarrif or tax on lead ammunition of certain types, make it more expensive than steel/copper projectiles, and there would be a natural drift away from it, whilst still giving a choice to those who must/want to use it and pay for it ?
Banning (making illegal to use) a metal in one context, gives power and will to think about the next ban, copper, steel and plastic wads, making the case that we need to 'prove' that they dont cause harm....
In effect they ban private gun ownership, because no one can use the ammunition designed for it, without actually legally banning them.