I don't see what relationship Reynolds 501 has with the introduction of TIG welding. 501 was introduced circa 1983 and all the early 501 frames that I'm aware of were lugged, with the notable excpetion of Peugeot's internally brazed model.

Likewise, the ecomonics of TIG welding itself were secondary. The prime reason for the for the adoption of TIG welding was the flexibility it provides in frame design, when not restricted by lugs. Developing lugs is very expensive and eliminating them provides great flexibility in both angles and tubing diameter and shapes.

The initial move to TIG was driven by ATBs. Originally, the slacker fangles favoured on ATBs forced many manufacturers to employ laborious and costly fillet brazing until appropriate lugs were developed. Then, in the mid 1980s, Rocky Mountain popularized the sloping top tube with their Blizzard model. The advantages of the extra crotch clearance was not lost on manufacturers and sloping top tubes became a standard ATB feature. However, rather than develop new lugs, TIG welding was employed to accommodate the non-standard angles. Manufacturers like Ritchey and Fisher also realized that, without the constraints of lugs, they could do things like laterally stiffen the bottom bracket by ovalizing the bottom of the seat tube.

Meanwhile, road bicycles primarily hung onto their lugs. The move to TIG welding on road frames occured as a result of another non-strandard design, the introduction of oversize steel tubing to increase ridgidity without increasing weight. In the very late 1980s, steel's reputation was begining to suffer at the hands of aluminum, carbon fibre and titanium, which were generally considered to be more advanced. Steel manufacturers fought back and one method was by taking the lesson learned from Kein's and Cannondale's oversized tubes. Rather than developing oversized lugs, TIG welding was employed, as most manufacturer's had experience from manufacturing ATB frames. The first major move came in 1990 with the introduction of the Diamnod Back's Expert TG and Master TG.

TIG certainly has added advantages in cost and weight but the prime motivator in its adoption was non-standard frame design, both in terms of geometry and tubing. It's outside my area of expertise but I wouldn't be at all surprised if the the original employment of TIG welding in bicycle frames dates to the late 1970s BMX explosion. Certainly, they had the rationale with their non-standard angles and gusseting. However, if so, there appears to be a rather large gap between its use there and it's adoption for ATBs and later road bicycles. Perhaps a forum member knowledgeable in BMX could enlighten us?