Except the bullet weight tends not to drop much, so you end up with a longer bullet with a higher ballistic coefficient and better ballistics.
If copper were as good or better, some shooters (competition, hunters) would already be using it. There is a reason why lead is used.
It’s the only metal over 10k kg/m^3 that isn’t radioactive, preciously expensive, or so hard it will destroy a rifle barrel.
As the other poster noted, Barnes-X. Been around a while and, not some, quite a few shooters are using them.
I haven't and don't care to be forced to.