Forget derivatives, they are not the problem
"An inquiry into what the real causes of the global financial crisis were using the logic of free-market economics"
While we're very happy to have you in the Gulch and appreciate your wanting to fully engage, some things in the Gulch (e.g. voting, links in comments) are a privilege, not a right. To get you up to speed as quickly as possible, we've provided two options for earning these privileges.
I just watch an otherwise boring story about the Medici. On their way to Florence, the party of merchants meets and old man who tells them that since they have been away, Florence has changed for the worse: No more to people concern themselves with the best wines and best olive oil, but with the best works of art; no longer do we trade by barter, but pursue coined money. Coined money was invented c. 600 BCE (and we are not quite sure why). It was also a derivative, since you cannot eat it. Basically, I agree with your larger analysis, only that this is an old story.
Bull kept at him but it was of no use. Hank just never had any new ideas after that.
"But, Uncle, didn't he just keep them to himself?' Jimmy asked.
"Yes, Jimmy, he never dare try or show his ideas again, lest Bull's gang made him give it up. The island got poorer and poorer even though Hank's island had the best ideas man of all islands."
"Productivity has a natural tendency to get better and will rarely decline-"
Long term, historical evidence does not support this point of view. This has only been true the last 200 or so years and mainly in the West.
Increases in the level of technologies is the ONLY way to increase real productivity. Historically, the rate at which technology increases has been slower than population growth, resulting in stagnant real incomes. Only with the advent of property rights for inventions, did this change.
Secondly, What is missed in your explanation is the complete "why" for the over-investment of housing. Changes in US patent law and the advent of Sarbanes Oxley meant it was much less profitable to invest in technology start ups, which is why the US was suffering stagnation in wages and productivity. This was throughout the rest of the decade. and so investors were excluded from a normally large sector and were driven into housing as one of the few profitable areas left.