Why does "at work" make as much sense as "working" in this sentence?

The phrase "at work" indicates a state in which the student is working at a job, not a generic activity. When someone is having dinner with the folks they are "at table". This is different than just being in proximity to furniture.

As a part of speech I don't have a better answer than yours but the difference is real.

I think the sentences mean different things. The first is ambiguous, it could be taken to mean that having students in the society is not working, whilst the second is clearly considering the work students do, or don't, put into it.

Your real problem, Elaine, is that neither sentence properly expresses the idea you are trying to express.

It is very odd to say that a student is not working. That is what students are supposed to be doing! It is also a little odd to say that a student is “not at work”. If she is in a lecture, then she cannot be ‘at work’ at that time. That would means she has a job and is ‘at work’ at the time. So I guess you mean ‘is IN work’ (= ‘has a paid job’). The fact that a student is not in work does not mean she is not a useful member of society.

Forgive me, but I think English is not your first language. The tell tale word is ‘the’ before ‘society’. In most European languages other than English and Greek, abstract nouns have the definite article in front them: ‘la vie’, ‘la vita’ ... So you cannot say “in the society”. You should say “in society”.

The better way of saying it is:- “Students, though not necessarily in work, are still useful members of society.”

“

"Working" generally implies active participation, You are doing something right now.

"At Work" means that the person in question is currently at a place where work is being conducted, though they could or couldn't be actually working at the time.

When preceded by "not necessarily", the statements following become ambiguous. Because of this, with both statements the implication that the students aren't actively participating (but are valued nonetheless) is being conveyed.