We do, it's just usually meaningless without specifiying the difference itself.
- We are the same.
- We are the disenfranchised.
- We are the lost.
- We are the different.
The first three make perfect sense, because they convey a complete message.
We are unified in that we are all [the same/disenfranchised/lost].
"We" is a group that is defined by a shared trait.
But the fourth example does not work this way. The message is not complete, we are missing key points of information:
- How are we different?
- Different from what?
- What does it mean to be the different?
It just doesn't make sense. However, if you wrap it in some context, it starts to make more sense:
Our new President has divided the country. He only listens to those who are the same as him. But we are the different.
This makes more sense. Essentialy, it means:
We are unified in that we are all [different from/ignored by our President].
It still sounds stilted, but it does convey a meaningful message, now that we know what "we" are different from.
Grammatically, there is no difference between
Fortune favors the bold.
Our society favors the different.
Here, it's not as stilted as in the previous example, because it's clear from the context that "the different" means "those who are different from the mainstream".