Why are transformers, stators and such made out of so many individual sheets of metal instead of one solid piece?

Because if not there would be a greater loss of energy.

You need iron for use in stators and transformers in order to conduct the magnetic current. The problem is that as the magnetic current passes through it one way it tries to induce an electric current perpendicularly to that magnetic current. If the stator, or whatever, is a solid piece of iron it will then create a huge flow of parasitic current which then essentially short circuits itself, heats up the iron core, and creates a huge energy loss.

But if the iron is made in plates separated electrically one from the other the magnetic current can flow through it one way and can't induce very much electric current perpendicularly. In each plate now a very small amount of parasitic current is produced, which is much more efficient than one huge parasitic current.

By making a transformer core out of laminated sheets instead of a solid piece reduces eddy current losses.

This is the one of the most important contributions of Tesla; minimizing "eddy" currents. By laminating the core with painted sheets or embedding ferric particles in ceramic etc, he created an efficient magnetic core that does not allow parasitic currents that waste power.

https://en.wikipedia.org/wiki/Eddy_current

To minimize eddy current losses.

TO REDUCE THE HARMFUL EDDY CURRENT EXISTS IN IRON CORE.