Why Do IC Specs Only List Voltage?
The Z80 datasheet you have linked to in your comments clearly shows on page 34

Icc1 Power Supply Current
4MHz   20mA
6MHz   30mA
8MHz   40mA
10MHz  50mA
20MHz  100mA

They are all rated for a Vcc = 5V

So, the way to read that is, this device will use this much current, at 5V, when the clock runs at these speeds.

It uses more current as the clock speed (which is driving it, with a crystal, or external clock source) is increased.

It is not symmetric. It does not run faster if more current is supplied. 

If the supply isn't capable of supplying enough current the IC will likely stop working correctly, and will not gracefully slow down.

So, among many other parameters, the datasheet specifies exactly how much current the IC uses, and under what conditions.

An IC is not a simple resistance. That device is thousands of transistors. It's actual current consumption will vary at a similar rate to the clock speed, i.e. its current consumption will vary within a microsecond. So trying to measure its current consumption is almost futile if you want to design a circuit using it. That is why the datasheet does specify its maximum current consumption, and operating conditions. It would be practically impossible to design a robust and reliable circuit using the part without that data.

Summary: Your 12A power supply will do it no harm. However, it isn't sufficient to have something capable of delivering that much power. The IC will also need a capacitor physically close to it, to handle that sub-microsecond current variation.