Predicate nominative is a noun or pronoun that follows a linking verb and refers to the same person or thing as the subject of the verb.
Here, mystery is a noun that links the subject people with the verb "are".
As , verb is in agreement with the subject i.e. Subject : people, Verb: are.
So, to link the verb and subject , singular form of the predicate nominative mystery ( which is a noun form) is used.
Because ,if we use plural form then the verb and subject cannot be agreed with each other.
Basically, here noun "mystery" works as an adjective as it shows the quality of the people.
So, it's apt to use the adjective form of the word "mystery" to make it a perfect sentence.
We can write like this : All people are mysterious, All people are heroic. This sounds much better as here the nouns perform the role of the adjective.