Specifically, all industrialised countries saw very similar developments, even though their politics differed vastly: https://en.wikipedia.org/wiki/Great_Depression#/media/File:G...
The US and United Kingdom happen to be rather close analogs to Germany. This isn't too surprising, considering they were already economically coupled, especially the financial sector.
In absolute terms, growth would seem to be roughly in line with making up not just the absolute losses during the Great Depression, but also factors in some modest growth that would have happened during that time. Population growth, for example, continued almost unabated during the 1920s.
Yes, they all experienced the depression around the same time, and if you just look at the signs of the slopes there's a lot of similarity.
However, the US was barely back to its pre-depression peak by 1940, while Germany was way higher. The only country in that graph that is somewhat comparable to Germany is the UK.
The basic "social democrat" mission statement, rarely heard these days even in Europe.
> why were democratically-oriented politicians unwilling or unable to take similar measures?
The short answer is that while politicians are dependent on the public for votes, they're dependent on a much smaller group of opinion formers, media organisations, and donors for everything else including winning those votes. And the small group tends to be wealthy, conservative, and not willing to have their economic freedom restricted.
The first years of the Nazi boom can of course be explained as recovery from the recent depression, but it seems that the boom went beyond that. And it's important to keep in mind that other countries didn't recover as quickly.
As for benefits to individuals, at the very least those programs created jobs. That is bound to have helped the living standards of many people.
Indisputably it would have been better to create jobs geared towards peaceful production. The question then is, why were democratically-oriented politicians unwilling or unable to take similar measures?
(And I don't mean that as praise of fascism. I mean it as a challenge to all those who consider themselves lower-case democrats: the job of democracy is to foster the well-being of the people. Stories like this article suggest that a lot more can be done on that front than we tend to see in contemporary democracies.)