Rustednuts,
Here is a story from experience:
I had a two seater 61 Scout that I used as a daily driver for years. Same problem with a worn rear axle bearing surface from a seized bearing. Could not find replacement axle, but a "friend" who worked at a machine shop made me a deal to weld up the worn surface and machine it back to original specs. Don't get me wrong, the repair "looked" beautiful to the eye. Little did I know what was hidden underneath.
It worked great for about 500 miles. Luckly, when my right rear wheel parted company with my Scout, rolled across four lanes of traffic and came to a rest on the opposite sidewalk, it didn't bounce off of any oncoming cars, or worse yet, off any pedestrians. Me on the other hand was able to make it to the right shoulder on the three remaining wheels and the emergency brake.
Once we got it towed back to the shop and had a chance to look at the break in the axle, it was clear that the break was clearly stress induced. It was also obvious that it started at the heat affected zone caused by the welding. In other words, the break was caused by the fix.
Every step in the manufacture of an axle from forging, heat treating and machining is geared toward achieving the greatest strength possible. I learned the hard way that welding an axle can create more problems than it solves.
