Sorry, pulling it through a mandrel does not change the molecular structure, it just changes the shape. It's not near hot enough. It becomes more rounder and more uniform - much more accurate and consistent, - good for hydraulic systems using a piston etc. The process of pulling and twisting through the mandrel work hardens it. It's much the same as bending it.
Hammering, squashing, folding it doesn't change anything on the molecular level either.
DOM is much harder to bend - that why it's often used for tie rods, control arms etc. But it also tends to shatter.
To prove or disprove it, simply put a piece of it in acid for a few minutes. The stress cracks become obvious - you can see the spirals where it was turned and pulled and all the tiny cracks around it.
Now bend it - - you are bending an already work hardened material - those stress cracks get bigger and lots more of them. It's not unlike bending a steel wire - then re-bending it at the same place. It becomes weak. The first bend is like the mandrel does to the tube, then the 2nd bend is harder to do since it's work hardened, and after the 2nd bend it becomes very brittle. A third or 4th bend it may even break. Try it!
Now weld it - even more cracks.
Put it in a press and you can break it.
It's so simple - use pool acid (Hydrochloric) or even Sulfuric acid.
To get rid of the stress cracks it must be heated then properly cooled - best to leave that to the heat treating boys. You aren't going to do that to a weld-in cage.
I've done it, and I've seen it. Talk to a metallurgical engineer about it.
I don't know about anyone else, but I sure wouldn't want to depend on something that's already pre-broken.
There are lots of opinions about DOM vs ERW - racing associations rules are often very different from each other. Many are based on wives's tales.
For example - most of them won't accept aluminum - yet when I owned part of Don's Chassis we specialized in Formula I race car chassis - that was all we did. Our world famous chassis' were all made of aluminum and carbon fiber. We had about 12 "engineers" working for us. Most specialized in the actual design of the structure, but 2 were metallurgical guys. By most racing clubs rules they would not be acceptable.
Welding itself even on ERW is a problem too. If it cools too slowly it becomes soft - annealed. To fast it gets hard and brittle. Try cooling a hot weld with CO2 gas or Freon - way too fast - it's easy to shatter, but it's so hard a regular hacksaw has trouble cutting it. Keep it warm with a torch and let it cool slowly, it stays soft and malleable. Try it!
But - proper design, triangulation, gusseting etc - is super important. Probably more important than the material itself - within reason. No, spaghetti won't work.