Ive had a thermocouple welder on my acquisition list for quite awhile, but they aren't all that cheap on ebay generally, and its not a very high priority, its factory automation and control engineering where they are doing hundreds per year Id imagine that it comes in handy, but then Ive also seen thermocouple "kits" with SS probes\wells, mineral insulation, and of course sensors.
The advantage there is you fabricate grounded, ungrounded ect packages yourself, but typically the sensor itself is factory made and you connect to it (which is where Id use a welder)
While I have no real idea of specifically what the difference would be between simply a wrapped vs welded vs factory fabricated sensor
I would assume its a closer repeatability with less error rate. and that a wrapped solution is a "close enough" general temperature type approach. Handmade welded sensors if they where subsequently calibrated and the error factor was coded into the aquistion system Id imagine would approach the same fidelity as a factory manufactured sensor that is consistently made from unit to unit in a more controlled manner. Simply with less error to plot those are "close enough" out of the box Id gues by at least a decimal place or two. (6.5 DMM)
Just a little dead reckoning