ALU in Minecraft, what can be achieved with this?

The first thing that comes to mind is a pinpad.

You owe the Internet Oracle a combination lock system for an iron door.

There is no application, any more so than any software virtual machine or emulator has any application. In short, anything that can be done with an ALU built in Minecraft can be done more easily and efficiently without playing Minecraft.

It may however, be less fun. Certainly, there is educational value in something like this, with the right teacher. But that's orthogonal to any sort of practical use.