That's basically true, but simplified. We also have homeless people in Germany, who don't own a washing machine. To get the government welfare, you have to navigate some bureaucracy: it's not hard, but there are still people who can't or don't want to do that.
About the house: If your house is cheap enough, I am not sure whether you have to use it all up completely. (I heard that there's even the possibility under certain circumstances of the government helping you with mortgage payments instead of helping you pay for rent.)
In general, you can live of the government welfare and even raise kids. But you need some skills for that, and they aren't that different from the skills that make for basic employability.
Do you have actual stats on this, or are you guessing?
Also, access to financial services (e.g. health insurance) is irrelevant. Financial services are intermediary goods (like education or business suits) - irrelevant by themselves, but sometimes useful to get other things you really want.
100% of poor people in Germany own a health insurance
0% own a house (you have to use up your own money first)
100% own a washing machine (paid for by the government)
50& own a car (my guess, but you dont really need it in big cities)