Like most things, there are limitations to what ever you are doing with something.
The original frame was designed with a lot of flex built into them, because they were designed to be low speed work trucks. They worked great if you loaded them up, and took the seed corn into the field at 15 mph, or made deliveries around town at 30 mph. Because they were built and designed to haul heavy loads, an occasional trip from the farm into the city wasn't much of an issue, but with the gearing, it was a 45-50 mph trip. High speed just wasn't on the radar for the truck designers of the day, they were work trucks geared and designed to move heavy loads from point A to point B.

I'm sure there were some guys using the truck frames in Gassers and going in the 10s (I'm betting they used the early 60s trucks rather then the early 40s trucks, design changes between the early 40s and the early 60s was huge). They did a lot of other stupid stuff back then as well! They got by because the Gassers were very light weight cars, using frames designed for heavy loads. I suspect the guys that were really running in the 10s were not using the original springs or the original spring mounts. Most of the frames were either reinforced with tubing (roll bars) or were so light weight the flex in the frame wasn't an issue, or they just dealt with it (or maybe they didn't know it was costing them speed). It was a time of innovation, some stuff worked well, some stuff didn't work so well. To assume just because the frames looked like an original unmodified truck frames from the 40s in pictures, that that's what they were, may be a huge assumption.

In answer to the original poster's question: What is the limit for mph with stock frame and suspension before going to modern stuff?
That is a good question! To be honest, that probably depends on how you feel about it. Assuming the frame is good and solid:

On the highway and streets, I doubt the frame itself is going to be an issue. Its when you want to start doing the hard, fast cornering (or fast drag racing) that the flex in the frame may become an issue, and that would be a limiting factor on how hard it will corner (or how fast it will leave the line), rather then will it be safe.

The suspension on the original trucks is leaf springs on all 4 corners. Though there are drawbacks to the ultimate performance capabilities to this design, it is a solid design. The issues in my mind are that 1) The springs are more narrow then modern springs, which could allow more side to side flex. 2) The springs were designed for hauling heavy loads, not ride quality. As such, the ride was stiff (understatement). You can remove leafs from the spring pack to aid in a softer ride, but that amplifies the narrow spring issue. 3) Since the springs are designed to carry heavy loads, the center bolt is nearly centered on the leaf spring. Leaf springs with the center bolt shifted more towards the front of the spring give better ride and have better control of spring windup on acceleration, both things were of little concern for the original purpose of the truck springs. 4) The shackles that attached the springs to the frame are single side pivot bars. They worked well when they were greased regularly, but the modern double shear spring mounting is much more stable and much more durable.

The rear axle had the tapered shaft brake drums. That alone is reason enough to replace it in my mind. Finding reasonable highway gearing is a very good second reason to replace it. Then you need to deal with antiquated brake design and finding replacement parts.

The front axle is a reasonably usable item. Its pretty simple. All it needs are good king pins (which may be hard to find) and modern brakes (disc or late 60s-71 drums) I prefer disc brakes. Sway bars can be added.

The manual steering box will require a big steering wheel or strong arms.

In my opinion: Modern brakes, a modern rear axle, and modern spring shackles should be present before an original frame gets a cab reinstalled. Unless the springs are really nice, modern springs would be present before it was on the road as well. I could live with a beam axle with good king pins & modern disc brakes.

Past that, if I think I want power steering or independent suspension, I'm building the truck with a modern frame that those things are already present on! Also, It the truck is getting big HP, the flex that was built into the original frame becomes a real concern for me. The last thing I want is to dump the clutch on a blown Hemi and have the frame twist into a pretzel! That may not have been a concern with the 60s Gasser guys, but I'm not one of them! Give me a frame that will transfer the power rather then one that will bow and twist in the middle. Gene