An alcohol lab thermometer is analog. And it functions based on the established properties of thermal expansion, which functions linearly based on temperature. Meaning that if you use RO/distilled water, and boil it for the high reading and put in ice water for the low, and record the barometric pressure and elevation (as you said), you can develop an exact bias curve for that specific thermometer. It will have that same bias curve from now on. You might need to make slight adjustments in the future based on the barometer, but those are minor.
It's so good because it's analog.
All thermometers need all the adjustments based on the bias curve of each one. But with calibrateable ones, the bias can be adjusted for. When you use a bi-therm (the metal dial ones), it suffers from the exact same situation as analog mercury/alcohol thermometers - the reading bias. But, unlike the lab thermometer, a bi-therm may develop different bias curves over time, especially as it is calibrated. So it needs to go through the entire effort or recalculating everything to be used as a standard, whereas with a lab thermometer, you just need to adjust for daily differences in the barometer.
With digital probes, they are actually more reliable, especially if of high quality and especially if the circuitry accounts for calibration fluctuations. But same sort of idea if used as a standard - the degree of drift may change, especially if a cord is kinked or it's dropped, or other some such. This rarely happens with good units and easy to spot by using two thermometers to compare.
Yes, there are good, reliable bi-therms, alcohol/mercury thermometers, and digital ones. Most of them are costly.