66 GPS channels for 22 satellites - why the factor of 3?

Adafruit Ultimate GPS is in no way representative of all GPS receivers out there. Many good receivers have more channels than that; 256 is common in high-end devices. Note that 256 is not divisible by 3, so the factor of 3 you're seeing is a red herring.

Also, you rarely get a signal from 22 satellites, and it's not necessary to have a fix. Having a signal from 7-10 satellites is quite common in real-world conditions.

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They way I understood it was due to the method the correlators work. As mentioned in the question, each satellite has its own unique code.

If you're starting up from the cold start, chip doesn't know which satellites are up in the sky, because it doesn't know the time and doesn't know where it is, so it needs to do exhaustive search. This is where having more correlators helps a lot. Instead of just loading expected satellites, you load as much as you can and then work from there on. This can be especially problematic for small devices with little or no memory on their own and no way to access the Internet for A-GPS.