A counter view, mainly because I don't like words like 'inevitable' and 'unstoppable':
1. The inevitable and unstoppable industrialisation of China
2. The inevitable and unstoppable industrialisation of India
Even rapidly-growing newly industrialising countries can have recessions. For instance Singapore for a year or two in the late 1980s. However recessions in China or India may well have a global effect similar to how the poor health of the US economy retarded our growth in the early '80s.
Also note Japan's situation; after faster than average growth for about 4 decades and a bubble in the late 80s they stagnated for years afterwards.
Though I don't think it's very likely for China, countries can and do go backwards, eg some South American nations were very advanced for a while.
Even if India and China fuel a boom (much like Japan did for the US in the 1950s and 60s) this cannot continue for more than 30 years or so, so what happens then? It could be Africa and South America's turn, though it's probably only Brazil that is populous enough to become a major power.
3. Perfect Capital Mobility
The capacity, that did not exist in the 1930's, for very large amounts of money to move rapidly around the world
4. International institutions
The UN, IMF, World Bank, etc. These are all forums for international discussion that did not exist in the 1930's.
5. International communications / travel
Greatly improved since the 1930's
There is this view around that we are becoming/have become a more internationalised economy and before that we were a self-contained backwater with nothing to do with the rest of the world.
But this is exagerated; colonisation 200 - 300 years ago was an act of globalisation. As was convict transportation, exploration, spices and gold mining.
And for most of the 1800s, the Australian-born proportion of the population was less than it is now, and our annual immigration intake as a percentage of our population peaked in Calwell and Menzies' time and has never since been higher.
Meanwhile, though Whitlam, Fraser and Keating are thought today as formers and champions of multiculturalism, and Howard an opponent (or at least lukewarm), the facts show that Whitlam, Fraser and Keating were 'low migration' governments while Howard has presided over high migration (though proportionately still much lower, is more diverse, than during Calwell/Menzies).
I don't have the figures in front of me, but I suspect that Australia's export:GDP ratio has been higher in the past than it is now. Since 1788, Australia was built on foreign capital while we exported raw materials to the world.
And the fact that there was a World War I and soon after a World War II indicate that much of the elements of globalisation were in place by the early 1900s (eg fast ships, telegraph and world-girdling empires).
Another evidence of early globalisation is the 1930s Great Depression itself; if every country was a self-contained autarky then the downturn would not have rippled around the globe.
Though it's been around for centuries, globalisation just feels more powerful now as the communication revolution and jet travel has extended it to ordinary people, rather than just big business (late 1800s), music or the movies (1920s -).
8. The nature of western societies
Now, more than ever we are consumer driven. We love to spend money and that is great for economic activity.
You haven't mentioned global resources and energy. Even ignoring grim greenie predictions, scarce resources will go up in price. If substitutes are not found then prices will rise, which may be inflationary yet retard growth.
9. The public sector
Possible expansion of / or massive capital works (roads, hospitals, dams, etc) - which it could be argued are needed anyway.
I think you're thinking of Rooseveltian 'New Deal' capital works projects to get the jobless working.
But in a global economy governments feel that they are under more constraints. For instance they might not wish to put up taxes to fund big projects due to wanting to be seen as a low-tax business-friendly administration and to prevent fragile depressed businesses from closing and laying people off. And if they don't put up taxes then they must borrow, which means higher future taxes.
The whole 'globalisation prevents depression' thesis relies on a global economy that is largely seawater with each country being a little fish hardly able to cause a ripple. But fish seem to watch other fish and once one gets shaking then a big wave might develop. So a big (internationalised) pond could be a stabilising influence (as you suggest), but it might not, as in the 1930s.
On the other hand a more isolationist view could see each countries being in their own watertight compartments, unable to influence the ocean. This could well protect them from depression caused by external causes. But on the other hand, protected backwaters unable to trade do tend to become poorer because of an inability to exploit comparative advantages.
Peter