The flaw in your logic is you can't increase the accuracy of the sensor itself by increasing the accuracy at which you measure the output of the sensor. All sensors have physical limitations to their accuracy. In the case of thermocouples, electrical noise and thermal noise in the sensor itself coupled with very low voltage output changes due to temperature limits its accuracy. At some point, increasing the accuracy at which you measure the output only increases the accuracy of measuring the electrical noise of the sensor itself.
Since thermocouples are non-linear, you must calibrate it over the entire range of the temperatures you intend to measure. This is the only way to get a one to one - temperature/ADC input voltage conversion with extremly high accuracy over the entire operating range. If you change thermocouples, you must calibrate it again. Most thermocouple circuits use a compensation circuit that "linearizes" the output of the thermocouple, but also reduces the accuracy. The compensation circuit can be built using the precision Op-amps needed to amplify the thermocouple output (see next paragraph).
Finally, ADC devices can't directly handle the low output voltage of thermocouples. They have their own accuracy limitations due to internal electrical noise. The thermocouple output must be amplified with a precision Op-amp which also have accuracy limitations due to internal electrical and thermal noise.
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