Well, when I finish building my Bearhawk, I would like to show in my builders log that all welds were crafted properly so my DAR gives me an airworthiness certificate. That coupled with the coin that I shelled out for my EAA class on welding leads me to believe that the pros know what they are doing.
It is physically possible to perform MIG welds on 4130, but if the joint is cooled too quickly, it will be a brittle weld. There is no other way about it. It is the nature of the steel because of the carbon content. The "41" denotes a low alloy steel containing nominally 1 percent chromium and 0.2 percent molybdenum (hence the nickname "chromoly"). The "30" denotes a carbon content of 0.30 percent. If you heat 4130 to the point where the carbon comes to the surface and then cooled too quickly (even a drafty garage is too quickly), it develops Martensetic qualities (a crystalline structure typical of steel containing carbon that has been heat treated) the weld will become brittle. If this happens, it has to be tempered just like tool steel or it will develop stress fractures and possibly break. An O/A flame weld has less tendency to do this
When welding an airframe, especially the clusters where there are lots of tube joints, there is a tendency for that area to become hot enough that the joint requires normalization. A MIG or SMAW welded airframe, if performed by a homebuilder, will not pass the DAR's inspection. This much I know.
Having a TIG welder at home would be nice, especially considering all of the welding that I do on my Wrangler and the parts that I fab for it, but I cannot justify the cost, especially since I dumped money into a lathe and mill. In fact, TIG welding is becoming the method of choice for homebuilt aircraft enthusiasts and when I am ready to start assembling my frame, I may consider buying one. For now, all I that I have been welding are the steel parts for the wing assembly (control surface/flap linkage/stick, etc) which are easily done with my O/A setup. Besides, torch welding has an almost zen-like quality about it
Some of the older builders swear by it. I have seen some older welders repair construction equipment in the field with nothing more than a portable O/A torch and a coat hanger and still make the weld look like a stack of dimes 
As for the friction welders? I could only wish 
I see, does Bearhawk specify in the builders manual oxyacetylene only, or can you TIG it? Cub Crafters and Maule might do some kind of normalizing or baking after thy MIG their airframes, all I know is that they do the actual welding with MIG.
BTW, not to hijack the thread too much, but which Bearhawk are you building?
I've dreamed about building one of the Super Cub kits, but most of them are pretty expensive (Cub Crafters wants $66K for the Carbon Cub kit, add engine, prop, avionics, paint, wheels and tires, and it's not much cheaper then their certified version

) Anyway, I've been wondering if the Bearhawk Patrol kit which is significantly cheaper is a suitable "cub-like" alternative. According to Bearhawks website it cruises quite a bit faster (less draggy) but I'm sure sacrifices STOL somewhat to do so. Probably still pretty good though. Honestly in my looking at them the only thing I wish the Patrol had was the jackscrew tail trim like the Cub.