As a new Berliner who immigrated here I can answer some of those:
- Berlin has a reputation for its artsy party scene and lax enforcement of drug laws. People come here in their 20s to let themselves loose.
- German universities are good quality and free for all (excluding the Semesterpauschale, but for my American or British friends this 300€ is basically nothing in comparison - especially when you count in the public transport ticket that comes with your student card).
- Immigration is hard, but you are entitled to permanent residency after you've contributed into the pension system for 5 years total within a continuous period of stay in Germany. People are willing to play the game with the Ausländerbehörde for some time if they know they will eventually become eligible for a permanent stay.
- Free, good quality healthcare. Agreed that Berlin is not the representative example in Germany, but for many people coming from places where healthcare is unaffordable or outright dangerous (I'd never want to go to the hospital in my hometown again), this is a huge change for the better.
- You can "get by" in Berlin with English only by now, although you'll be highly dependent on others. I know people who've been here for 5+ years and still struggle to order a beer. Not the best way of living, but definitely possible with so many other expats around.
- Prices/earnings ratio is still better than in many places in the West.
I chose the city myself because I already knew the language (mandatory second language after English at school in my home country), and I don't regret it. You can navigate around the coarse edges and live a good life in here.