Agree with your criticism about 'many modern economists'.
But what the New Deal did was it stole, via taxes, money from productive businesses and gave it to the unemployed to create useless earthworks and money loosers like the TVA (Tennessee Valley Authority). This is bad economics. Creating entitlement programs, taking money from productive businesses that would be hiring and giving it to people for no reason is bad economics.
It had lasted 2-3 years before Roosevelt took office and you had Hoover raising taxes from 25-65% (or whatever it was)... which further deepened it. This is not often cited, which was why I think it is important.
To raise the top rate to 65% during peacetime? Especially right after the market crashed? This, more than anything, probably exacerbated the GD.
Roosevelt also launched massive farm subsidies during this period, yet people were starving. Stealing money from teh rich to raise teh price of grain for everyone.
I understand what your saying about the credit problem, but don't see how raising taxes and redistributing wealth and creating entitlement programs helps this.
The problem that was faced in the great depression was a structural problem. Because of the collapse of credit and the impact on the economy, there was a sharp decline in jobs. Because of the sharp decline in jobs, there was a sharp decline in private demand. Because of the drop in private demand there were further declines in jobs.
This is a classic monetary depression that Milton Friedman wrote about so well.
When, because of a collapse of credit, there is no private demand, you cannot stimulate the economy by creating more credit because no one wants it to invest to create jobs (Japan has been going through that problem over the last several years, and it is only the very strong hand of government that has prevented a monetary crisis turning into massive unemployment).
The only way to get money into the hands of private parties to increase demand is to print it and put it in the hands of those who you wish to start spending. That is exactly what the New Deal did. But, because Roosevelt recognized the danger of just handing out money, he created jobs programs and made people do some sort of work to earn their handouts.
The subsequent fate of such programs as the TVA or the Bonneville Power administration, and such losing money because they sell power at below market rates has nothing to do with the New Deal. It has to do with Congress not being able to bite the bullet and make these operations charge market rates (their industrial consumers such as the aluminum and aircraft industries very much enjoy paying lower than fair market value for electricity.)
That you cannot cut a government program once it has been created is the fault of our current politicians, and not the fault of the creators of the program.