Cpu needs heat sink to conduct heat away before any thermal runaway happens to burn out the expensive cpu.

The concept of thermal grease is to avoid dead air space, between cpu and heat sink. So that conduction of heat transfer is uniform and efficient on the full surface of the cpu.

There are many types of thermal grease, but the best is silicone grease(liquid). After a few month however, silicone will dry up and the cpu may run hotter. When computer suddenly slow down, you must inspect thermal grease if it has dried up, and reapply more grease freshly.

The question of thickness of thermal grease was never answered. Usually the spring retainer pressure will equalize at certain thickness. But you could wiggle the heatsink and flatten the thickness for better contact after some shear applied between cpu and heat sink.

Avoid waxy type of thermal grease, which has to be melted to be effective. Cpu heat will melt the wax, then cooling becomes effective by the heatsink.

Carbon fiber carpet type has to have silicone soak thru the carpet to be effective heat transfer media.

Silver additives in epoxy should be avoided. Epoxy is cemented in place and heat sink and cpu can not be separated without some damage.

That leaves good old thermal grease with zirconium oxide which may dry up a little; and freshly reapply is a chore.

Otherwise, watch the cpu temperature, the burning-in by daily use may lower the operating temperature, but if usage ups the temperature, then thermal grease has to be inspected before any catastrophy happens to your cpu.