Yes, it's not paid to everybody, but everybody can rely on it. UBI is technically for everybody, but the average person that does work will not feel a difference in most scenarios, as increased taxes will eat the UBI that's paid out.
As for the stigma associated with not working: true, but it's not part of, or encouraged by, the law. It will be the same with UBI, it will not be admired to not contribute to society. Some people may feel that they do in fact contribute, but society at large values other things than self-actualization.
The university/higher education system is weird, but for other reasons (my personal theory is that you can't have organized bureaucracy in Germany without some senseless cruelty). It's another point on the board for "free doesn't necessarily give you the expected results" though: unlike in the US, it's free, our "student loans" (Bafög) are generally interest free and 50% of the amount owed will generally be forgiven. Obviously, we see plenty of people entering, but we don't see the results you'd imagine if costs were what's holding people back.