There are a number of different CPU cooling pad designs. The most appropriate design to use will depend on the CPU and motherboard configuration and the available budget.

ZIF

because of their design

A CPU works off of DC voltage. If you monitor the current draw of a CPU, it will likely not be DC, since a modern CPU is a CMOS design, current is only drawn when transistors are switched (ignoring the small leakage current). This is why overclocking (forcing the transistors to switch faster) can cause the CPU to overheat, and why "power save" mode on a laptop sometimes slows down the processor speed.

cache is more expensive and it will increase the cost of the system terribly.

processing of more than one cache will complicate the design of CPU and increase the burden on CPU.