"I do think universities should have a duty of care to its students though."
But, what is that level of care? It's not a school, university staff aren't substitute parents. It's not a family environment and it's a completely unrealistic expectation to think it could be.
Let's say you get to the point of being able to fund an enforced knock on the door every single day for every 17-25 year old (both on and off campus) whether they agree to it or not.
Ignoring the cost and how intrusive many would find that, what if they just lie when they answer the door? Or don't answer because they're sleeping elsewhere or are in a class or have headphones on? When do you force entry? How much do you chase them up? How are you supposed to know everyone's patterns? How are you supposed to spot clinical depression in many people you don't know, when people miss it in their own family members and friends?
Where do you draw a line of being parental? What if they're not depressed but you think their boyfriend looks aggressive and dodgy, or they seem to keep getting drunk and living in squalor?
Meanwhile are you noting all this stuff down routinely in a database for whoever takes your job next cycle to know? What happens to their privacy?
And when students are clearly not fine, when there are serious, serious mental health concerns, what are you supposed to do if they refuse to cooperate?
Short of sectioning them (which I couldn't with an active suicidal family member), you're stuck. You can't call parents under data protection and that's assuming they have supportive family to begin with.
Like others I'm really not trying to be difficult but either we agree as a society that these are adults who are capable of being at university and living alone, or we don't. If they're not then what?