A couple of things: First, the study was done by folks who build houses (not construction workers, the people who pay them). I'd like to see something by a dispassionate party that has nothing to do with the industry. Second, it was "government at all levels" which makes it meaningless. Missouri's regulations don't affect the price of a house in Illinois, and my guess is that most of those regulatory cost increases were at the local level in expensive towns, probably in California.
I'm glad that you realize that regulation is necessary, but I'd like to see which regs they're talking about. A couple of years ago they were talking about mandating sprinkler systems in new homes here in Springfield, which would raise the cost a lot but at the same time make them safer. They shelved the idea after public outcry.
They use to use lead paint, now outlawed, and with costs but also good reason. Safety equipment and training for construction workers costs; roofers didn't use to be required to use tethers. That slows the work down, which raises the cost, but IMO is a GOOD regulation.
How about that cancerous Chinese flooring? Company had to rip it all out, at huge cost and yes, a necessary one.
All in all, the article is propaganda. Like you say, some (I'd say most) regulations are good. I remember rolling up the windows in hundred degree weather when driving past the Monsanto in Sauget before cars (or many homes) were air conditioned, because the air burned your lungs. I remember Dead Creek in Cahokia catching fire. The clean air act and clean water act solved both those problems. My grandfather died because there was no OSHA, so Purina didn't have to put doors on the elevator. Again, paying an extra 25% to keep workers alive is a cost I'm greatly willing to bear.