My comments are based on qualifying many welders for many years. Too many years to admit to.
I have found the problem to be so pervasive that I include a requirement in the project specification that all welders pass a simple fillet weld break test. The test consists of a single pass fillet weld with a 5/16 inch leg with a stop and restart about midway along the length. The ends of the test sample are cut off and the remaining 6 inches fractured through the root.
My experience with groove welds is that about 85% of the experienced welders pass the grooved plate test. My experience testing welders with the simple fillet break test is not as good. The failure rate is on the order of 85%. In some shops the failure rate is higher yet, approaching 95%.
Even when the welder shows me a copy of his/her qualifications for a grooved plate, I still require the fillet break test. The failure rate should be cause for anyone to take notice.
If you have a fabricator that insists there isn't a problem with single pass fillets using small diameter electrode, let them show you by having a few welders, selected at random, weld a couple of T-joints. It they know what they are doing it will take about fifteen minute to weld and break. You don't have to cut the ends off, just weld and break. A quick check of the root (they are required to have fusion to the root, but not necessarily beyond) is one attribute you are looking for. You are also checking to see they have good starts and stops, i.e., craters filled to their full cross section, legs that are nearly the same dimension (5/16 inch is the required size), a weld face that is not excessively convex or too concave, slag inclusions that exceed the allowable, etc.
As I said, the test shouldn't take more than fifteen minutes start to finish. If they pass on the first attempt, keep that fabricator. When they fail, and I put my money on they will fail, you have a good reason to ask them to requalify all their welders using the “simple” fillet break test.
Best regards - Al