Why do we need constructor chaining in the same class instead of using methods?

Question

I was learning about constructor chaining and I got two cases. One is to initialize the parent classes which is okay. Java by default calls the constructor of the parent class and we can use super if we want.

The other case which I got was related to code redundancy. Below is an example.

class Student {
    int id;
    String name, city;

    Student ( int id, String name, String city ) {
        this(id, name);
        this.city = city;
    }

    Student(int id, String name) {
        this.id = id;
        this.name  = name;
    }
    
    void display() {
        System.out.println( this.id + this.city + this.name);
    }

}

// The above example is nice and I can see that I didn't have to write the code for initializing name and city but the same code can be written as below

class Student1 {
    int id;
    String name, city;

    Student1 ( int id, String name, String city ) {
        this.setStudent(id, name);
        this.city = city;
    }
    
    private void setStudent ( int id, String name) {
        this.id = id;
        this.name = name;
    }
    
    void display() {
        System.out.println( this.id + this.city + this.name);
    }
}

I am trying to understand if there is any specific use case where we would need constructor chaining and initializing with method style won't be applicable. If not then what is the advantage of one over the other or why the constructor chaining is preferred?