I don't believe DH7 really applies here, because the status quo is the steelman of your proposal for change. We already have open-source financial analysis and financial models, and mathematicians do work in the industry. I'm unclear on what concrete changes you're actually proposing here that haven't already been implemented decades ago.

1) I suspect this is the reason why Simons is so unusual, and one of the main stumbling blocks to your plan. Getting to high levels of mathematical skill and achievement takes years, and spending more years learning finance is naturally going to be unappealing. Surely they won't all make $10B, and trying to get folks who've spent their lives getting the famously conservative institution of tenure to give it up for the famously chaotic world of Wall Street seems like a serious challenge.

2) I would agree with this - mathematics is a frame of mind as much as anything, and a pretty useful one. While finance has some elements of the same effect, "anything can be traded" is far less transferrable, and the more specific knowledge base lacks the out-of-field utility of math.

3) True, but then that's true of most fields where people want to do a good job.

4) I'm not convinced of that. One of the good things about finance is how incredibly well incentives are aligned(modulo Congress) - someone who guesses right makes billions, someone who guesses wrong loses billions. Having managers share information and analysis destroys that accountability. It also would tend to encourage groupthink - 20 separate paths of analysis will inherently vary more than one collective pool of analysis. Given that groupthink is a major contributor to bubbles, this seems a real danger.

5) Granted.

6) The primary cost is going to be reduced tax receipts and increased welfare costs, plus the stimulus. The bank bailout actually made a small profit, the auto bailout would probably have happened either way by now, but the damage to the economy(especially the top strata that pays a disproportionate amount of the taxes) really did hurt the government's finances. Also, for ease of data collection, I'm limiting my numbers to the US. Most developed economies will have a similar money lost:GDP ratio(Canada and Japan less, PIIGS more, but it's assumed to work out in the end). All numbers from this wonderful document: http://www.gpo.gov/fdsys/pkg/BUDGET-2014-TAB/pdf/BUDGET-2014-TAB.pdf

Tax receipts: We'll measure these peak-to-peak, so 2000-2007, and use that to establish a trend line. In 2000, the USG took in $2025B, in 2007 it took in $2568B, for an average growth of 3.45%. We'll assume that inflation and population growth are constant over the time period, so the trend will stay flat.
Year Trend Actual Loss
2007 2,568 2,568 0
2008 2,657 2,524 133
2009 2,748 2,105 643
2010 2,843 2,163 680
2011 2,941 2,303 638
2012 3,043 2,450 593
That's a cumulative loss of $2687 billion in tax receipts thus far.

Social spending: It's hard to define "social spending" precisely. Social Security, for example, should remain basically stable during economic change, while food stamps will vary wildly. I'm going to use the "Income Security" function and "Health" function(which is primarily Medicaid - Medicare is separate) to approximate this. There's some stray charges in there(federal employee pensions, occupational health and safety, etc.), but those should be fairly stable modulo recession, and I don't know enough about what precisely is in the categories to get too fine in my distinctions. I'm using the same 3.45% growth assumption.
Year Trend Actual Loss
2007 632 632 0
2008 654 712 -58
2009 677 868 -191
2010 700 991 -291
2011 724 970 -246
2012 749 888 -139
This yields a total of $924 billion in added welfare costs.

Stimulus: The ARRA was estimated at $831B of total costs, though a significant fraction of that has been counted above - $288B was tax cuts, $155B was health spending, and $82B was welfare of various sorts. The remainder is $306 billion on education, infrastructure, and research.

The sum of the above categories is $3917 billion, to the end of FY 2012. However, we also need to factor in the effect of lower interest rates - we're spending less on debt interest today than we were in 2006, despite a 137% increase in the size of the debt. This works out to a $228B savings versus trend(again, assuming 3.45% YOY growth). Throw in a few miscellaneous billions for uncounted programs, we can estimate the cost to date at $3.7 trillion. Final cost will likely be some $6-8 trillion, depending how long this mess continues for.

It's worth noting, though, that if you phrase it in terms of cost to taxpayers, the loss of receipts shouldn't really be counted - after all, it doesn't lose me money to have my taxes go down. Actual new spending as a result of the recession is only about a trillion thus far, the remainder is simply deferred taxes.

(Yes, these numbers are a bit ham-fisted in places. I'm not the CBO, I don't intend to get too far into the details for the sake of an internet discussion. It's a good enough estimate to work with)