Thermocouples have a small variance in the voltage they output so you need something like the MAX31855 to amplify it. An Arduino has a precision of 1024 values between 0V and 5V, and, as an example, a K thermocouple only puts out ~3 millivolts at 160F.
You should probably explain that it the info you just posted above does not apply to the Max31855 because it has an amplifier and
transmits digital so the analog input capability of an arduino is completely irrelevant when using the max31855.
It does however provide a good comparison of what you would be struggling with if you didn't have the 31855.