This is completely untrue. Hoover was a reknowned disaster-management expert and very much intervened when the economy started collapsing. He raised taxes to try and balance the budget, he enacted price and wage controls, he signed the Smoot-Hawley tariff, and began various public works programs. Hoover did not believe in laissez-faire capitalism. If Hoover's response had actually been laissez-faire, then the economy might not have spiraled into the depresison the way that it did. One of the prime reasons why the economy did what it did was because of terrible monetary policy at the Federal Reserve, but no one really understood this at the time. We also had a much more limited understanding of macroeconomics at the time.
Government had nothing to do with the population gaining prosperity, that was due to the market economy. Government can play a role in facilitating the market through infrastructure or funding research, but government itself is not what caused people to rise up from being destitute. And while government does have some roles to play, it also has a huge record of very negative effects from doing things as well.
A big government is not required for adequate regulation. An economy needs, overall, light and efficient regulation. Regulation is one of the means by which corporations "rape the middle class," if you will, as they use regulation to establish cartels, to drive smaller competitors out of the market, to force people to buy more expensive light bulbs as we've seen recently under the guise of being "green," and so forth. Regulation is a tricky subject because with too little of it, businesses will abuse people. And with too much of it, businesses will abuse people. That is why Republicans are for limited government. Not anti-government, but limited government.
Single-payer healthcare is not the ideal form of universal healthcare because it is socialist and as such, is fraught with the problems of rationing. The British system has this problem, the Canadian system has been experiencing it, other European countries have partially privatized their healthcare systems because of the rationing problems.
They also are very small and very uniform and don't have much in the way of defense spending. Take Norway, Denmark, or Sweden and crank up the population by 30X, add in a whole slew of additional cultures, ethnicities, races, religions, languages, etc...and you'll find they don't function nearly as smoothly. And Norway, BTW, gets 25% of its GDP from oil exports. It is one of the world's largest oil exporters.
BTW, why is egalitarianism always viewed as some noble end to be sought after? It's fine for a society to strive to have a safety net, but otherwise, freedom and opportunity should be the goal, not "egalitarianism" where we all come out equal in the end.
You might want to look at just what FDR did during the New Deal, as much of it was utterly disastrous statist economic policy that lengthened out the depression. Government is mostly incapable of stimulating an economy in the short-term. Long-term, it can facilitate economic growth, which the New Deal did, but this would be years later.
World War II spending did not get us out of the Great Depression. What ended the Depression was a few things:
1) The rest of the industrialized world had been bombed to ruins and was re-building. The U.S., meanwhile, had not only not been bombed, but not made up a massive chunk of the world's total industrial capability.
2) Some countries followed the path of socialism, which was disastrous, such as the UK.
3) The New Deal's infrastructure programs - the New Deal had some bad aspects, but it did contribute to the post-war economic recovery in terms of the infrastructure. The infrastructure programs did not stimulate the economy during the Depression itself, but after the war, they allowed for whole areas of the country, which had previously been rural backwaters, to develop into booming, thriving economies, because of roads, electricity, airports, bridges, etc...
4) The defense budget. The U.S.'s defense budget served as a major form of industrial policy after the war by providing funds for research into various industries. Things ranging from the C programming language, C++, and Unix, to the laser and transistor were all developed at Bell Labs, with funding from DARPA. The Internet and GPS both stem from military spending. The AEGIS air defense computer and the Apollo spacecraft computer contributed to the development of computer architecture. All of these technologies led to the creation of booming industries and lots of economic growth in the economy.
5) The Interstate Highway System - another infrastructure project, one which was also tied to national defense, so we'd have the ability to move the army from one side of the ocuntry to another easily if need be. The IHS has had a huge economic impact on the nation since being constructed.
6) During the Great Depression, the birthrate declined. By the time the end of World War II rolled around, the men who had been born during the Depression years, many of whom were just entering the job market, found jobs ready and waiting for them.
FDR did not have the nation tread water, he basically anchored the country underwater, until finally after the war, the various things he'd done that were constraining the economy, were lifted. Also, why would nationalization have saved the economy during the Depression (it actually was quasi-nationalized due to FDR's policies, which hampered economic growth)?