The prevention of rust does slow scale accumulation because rust is a rough porous surface that scale likes to stick to. But other than that (anodes also are rough porous surfaces) I'm not aware of any way they actively reduce it. Maybe the electronic ones, but that's out of my wheelhouse (and they aren't sacrificial).
The sacrificial anode is there to protect the steel tank. It lasts a long time.
This is a hard water problem as everyone else is saying, and a water softener would solve the issue.
*Edit: check the very bottom of your tank since you have the elements out. It most likely has a pile of calcium and other minerals sitting on the bottom.
In NA, steel is standard. I've never seen a copper hotwater tank in Canada. I think that used to be somewhat common in Europe, but copper is freakin' expensive now so that's gone by the wayside, as well.
Copper would cost a lot more than a rod. Water is weird and will attack the ‘weaker’ metal first(somebody will probably have a better word for that). Hence the sacrificial part of its name. As long as you replace that part when it needs it the steel tank won’t rust.