The term is "unlimited", not "limitless".
D1.5 is the Bridge Welding Code while D1.1 is the Structural Welding Code/Steel. The welder qualification requirements with regards to how the test is administered are more stringent in the bridge code.
D1.1 has no restrictions regarding the use of power tools for cleaning the weld beads between weld passes. The welder can change the weld bead profile to eliminate ropey beads, undercut, slag inclusions, etc. The bridge code on the other hand does not permit the use of power tools for cleaning and it doesn't permit changing the weld profile between beads.
The acceptance criteria is the same, so I don't see where the Owner wouldn't accept qualification to the bridge code. I can see why qualification to the structural welding code is not acceptable if the bridge code is the governing document.
Al
Check out 4.2.2.1 in the D1.1
"Previous Performance Qualification. Previous performance qualification tests of welders, welding operators, and tack welders that are properly documented are acceptable with the approval of the Engineer. The acceptability of performance qualification to other standards is the Engineer's responsibility, to be exercised based upon either the specific structure or service conditions, or both."
I could be wrong but I think that means that you could be approved by the engineer to do the welding but it wouldn't necessarily get you a certification.