Let me open by saying I’ve been testing welders for, well, let's just say a long time. I also welded for over twenty years in the shop and in the field on both structural steel and pipe.
The skill set need to weld structural steel differs from that needed to weld pipe. Many of the welders experienced welding pipe struggle to pass the structural qualification and structural welders struggle to pass a pipe test. Pipe welders tend to weld with lower amperage simply because the wall thickness of the pipe is relatively thin. The structural welder is welding members that are much thicker and require higher amperage. Pipe welders, limiting the conversation to shielded metal arc welding on ferrous metal, often weld open root pipe joints where the electrode is typically a cellulose based flux covered electrode at low amperage using a whip technique. The whip technique isn't recommended when welding structural steel using a low hydrogen electrode.
I've tested many welders transitioning from pipe to structural and vice versa. Both struggles to make the transition because different electrode types are used, amperage ranges are different, and the techniques are different. It isn't to say it is impossible, but it is surprising how many welders can't make the transition without practice.
You mention that most of the structural welding consists of fillet welds as if the fillet weld isn't that difficult to deposit successfully. Over the last twenty years or so I've always included a requirement that the welders pass a "simple" T-fillet break test before welding on my projects. The failure rate is surprisingly high and most welders fail due to incomplete fusion in the root. If one was to "believe" the codes, a welder qualified on a groove test is automatically qualified to weld fillets, yet many welders cannot pass the fillet weld test without coaching and practice. My experience has been the pipe welders struggle more than the structural welder because the pipe welder is more accustom to welding with low amperage and using stringers. When the pipe welder takes the plate test with backing, a typical problem is securing fusion in the corners of the root between the groove face and the backing. Once again, the problem is typically using low current and using a slight weave in the root.
With regards to the simple fillet weld, I asked my professor while I was a student taking my structural design courses, why the size of the fillet welds most often specified were ¼ and 5/16-inch? His response was because that size is relatively easy to deposit with large diameter SMAW electrodes. That statement is perfectly logical and true. As I worked my way through college I worked as a welder in a fabrication shop and we welded with 3/16 and ¼-inch diameter electrodes day in and day out. That is no longer the case. Flux cored arc welding and gas metal arc welding are the welding processes of choice in the modern fabrication shop. The electrode diameters are much smaller and some manipulation is required to deposit a ¼ or 5/16-inch fillet weld in a single pass. The fact that the welder must manipulate the electrode is the problem. If I see the welder making circular movements with the electrode, there is a high probability the welds are not fused in the root. The same is true in the field if the welder is trying to deposit large fillet welds in a single pass. By the way, if the welder isn’t using low hydrogen electrodes, there are minimum sized fillet welds that must be deposited as single pass weld per the AWS structural welding code/steel. Once again, it is all about the technique used by the welder to make those large single pass fillet welds and using sufficient welding current.
The bottom line is the Engineer (the Owner’s representative) has the authority to allow welders qualified to a different welding standard to weld structural steel without being requalified. You are correct when you mentioned that a lot of engineers do allow welders qualified to ASME Section IX to weld on structural work. It makes my job as an inspector more challenging, but oh so much more profitable.
If you have any doubts, simply have your welder take a simple T-fillet break test. It is a single pass 5/16-inch fillet weld on one side of a T-joint consisting of ½ x 4 x 8-inch plate. If the welder knows what he’s doing, it is a 15-minute test. If the welder can’t pass that simple test, do you really want him or her to be welding all those fillet welds on your project? Remember, as mentioned, structural welds rarely get more than a visual examination. I don’t know many people, other than Clark Kent, that can see whether there is proper fusion in the root of the fillet weld.
I look at it this way; I wouldn't go to a brain surgeon to get a colonoscopy and I wouldn't go to a proctologist for brain surgery. Both are doctors, but their areas of specialization are at different ends of the spectrum.
Best regards - Al