Why are transformers cores made of iron and not nickel, when the relative permeability is higher for nickel?
Transformer laminates are actually made from silicon steel and that raises the electrical resistance of iron to about 5 times greater hence, eddy current losses are much reduced by using silicon in the mix.

For nickel the electrical conductivity is 1.43 x 10^7 and
Iron is a bit higher resistance with electrical conductivity at 1.00 x 10^7.

Adding the silicon makes transformer laminate silicon steel about 7 times more resistive than nickel.
Magnetic saturation is also improved over nickel too: -

Magnetization curves of 9 ferromagnetic materials, showing saturation.

Sheet steel,
Silicon steel,
Cast steel,
Tungsten steel,
Magnet steel,
Cast iron,
Nickel,
Cobalt,
Magnetite

Compare (2) silicon steel with (7) nickel.
Graph courtesy of wikipedia.