Error when working with pointers in insertion of a node in a binary search tree

So I have the following code:

#include <iostream>
#include <vector>
#include <cstdlib>
#include <ctime>
using namespace std;
struct Node
{
    int value;
    Node *left = NULL;
    Node *right = NULL;
    Node(int value)
    {
        this->value = value;
    }
};
struct BST
{
    Node *root = NULL;
    void insert(int value)
    {
        cout<<"Inserting: "<<value<<endl;
        Node *current = root;
        while(current != NULL)
        {
            cout<<"YEA";
            if(value > current->value)
            {
                current = current->right;
            }
            else current = current->left;
        }
        current = new Node(value);
        cout<<"In the node val: "<<current->value<<endl;
        if(root == NULL)
        {
            cout<<"Root is NULL but it shouldn't\n";
        }
        cout<<"Root val: "<<root->value<<endl;

    }
    void remove(int value)
    {
        Node *toReplace = NULL;
        Node *toBeReplacedWith = NULL;
        toReplace = search(value);

        Node *current = toReplace->left;
        if(current == NULL) toBeReplacedWith = toReplace->right;
        else
        {
            while(current->right != NULL)
            {
                current = current->right;
            }
            toBeReplacedWith = current;
        }
        current->value = toBeReplacedWith->value;
        current->left = toBeReplacedWith->left;
        current->right = toBeReplacedWith->right;
        free(toBeReplacedWith);
    }
    Node* search(int value)
    {
        Node *current = root;
        while(current != NULL && current->value != value)
        {
            if(current->value > value) current = current->left;
            else current = current->right;
        }
        if(current == NULL)
        {
            cout<<"The node didn't exist in the BST";
        }
        return current;
    }
    void traverse()
    {
        rec_traverse(root);
    }
private:
    void rec_traverse(Node * current)
    {
        if(current == NULL) return;
        rec_traverse(current->left);
        cout<<current->value<<endl;
        rec_traverse(current->right);
    }
};
int main()
{
    BST tree;
    for(int i = 0; i < 10; ++i)
    {
        tree.insert(i);
    }
    tree.traverse();
    return 0;
}

Can somebody tell me why when inserting an element the root still points to NULL instead to a Node instance? I even check the current pointer for a value and it has but still for some reason root is NULL when it should be the first node to be assigned a value