You are very much ignoring a lot of historical developments that lead to the situation that Berlin is in. Berlin used to be an industrial powerhouse, many well-known companies were founded there - Siemens for example. Borsig, Varta, Osram, ... had large factories in the city. However, after WW2, Berlin was divided and the western part hard to reach, so most companies relocated, most industries disappeared. Siemens moved headquarters to Bavaria. Despite all the self-inflicted problems that slow economic growth, the expectation that Berlin could or should be on par with other capitals is problematic.
It’s notable, but the question of why that is so and whether that’s problematic is not as clear cut as it seems to be. For example, germany has a traditional industrial base that consists of mid-size, often family-owned businesses. We even have a word for it - Mittelstand. Quite some are world-leaders in their field. Whether that’s a good or a bad thing is certainly open for debate, but it’s not as simple as “no unicorn startups in germany - fail.”
GDP is weird. For instance, private healthcare pushes GDP up, but I'm not sure Germans would like to have a higher GDP and pay a bunch more for healthcare in a market like situation.
More generally, if you look at Europe there are actually far more startups. They generally have much lower valuations though, because there isn't as much capital going into VC.
And probably you should look at Sweden as it does better than the US on a per capita basis in terms of startups.
Actually Germanys economy is very differently structured than the US. A significantly larger portion the GDP is coming from relatively small companies (called Mittelstand in German). Those companies also often invest very large percentages of their revenue into R&D (typically much more than the big cooperations). For example a significant portion of worldwide advanced manufacturing is powered by relatively small German companies that nobody ever heard about,
