Are welded-handled stock pots safe?
Assuming that there were stock pots manufactured with handles that broke off, they would likely have been recalled by the CPSC.  

It appears that the CPSC has only ever recalled one stock pot that was based on a single report of a handle breaking off.  The problematic stock pot was sold by a liquidation company.  Based on this, I'd assume that any NSF certified stock pot that you buy from a reputable retailer is going to be safe.