Well, the great depression was something different because it had already lasted may years before Roosevelt took office. It had already proven itself impervious to the normal efforts to expand credit which assumes that there is someone wanting to expand his business and will do so upon the supply of credit on acceptable terms. When no one is credit worthy and no one can put together a sound business plan for expansion because he has no potential customers, then you have a structural problem which requires a different kind of solution than the one the interest rate technocrats can provide.
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.