Decorator Design Pattern in C++

I have found this decorator design pattern on the internet here :

// CPP program to demonstrate
// Decorator pattern
#include <iostream>
#include <string>
using namespace std;

// Component
class MilkShake
{
public:
    virtual string Serve() = 0;
    virtual float price() = 0;
};


// Concrete Component
class BaseMilkShake : public MilkShake
{
public:
    string Serve()
    {
        return "MilkShake";
    }

    float price()
    {
        return 30;
    }
};

// Decorator
class MilkShakeDecorator: public MilkShake
{
protected:
    MilkShake *m_MilkShake;
public:

    MilkShakeDecorator(MilkShake *baseMilkShake): m_MilkShake(baseMilkShake){}

    string Serve()
    {
        return m_MilkShake->Serve();
    }

    float price()
    {
        return m_MilkShake->price();
    }
};


// Concrete Decorator
class MangoMilkShake: public MilkShakeDecorator
{
public:
    MangoMilkShake(MilkShake *baseMilkShake): MilkShakeDecorator(baseMilkShake){}

    string Serve()
    {
        return m_MilkShake->Serve() + " decorated with Mango ";
    }
    float price()
    {
        return m_MilkShake->price() + 40;
    }
};


class VanillaMilkShake: public MilkShakeDecorator
{
public:
    VanillaMilkShake(MilkShake *baseMilkShake): MilkShakeDecorator(baseMilkShake){}

    string Serve()
    {
        return m_MilkShake->Serve() + " decorated with Vanilla ";
    }
    float price()
    {
        return m_MilkShake->price() + 80;
    }
};

int main()
{
MilkShake *baseMilkShake = new BaseMilkShake();
cout << "Basic Milk shake \n";
cout << baseMilkShake -> Serve() << endl;
cout << baseMilkShake -> price() << endl;

MilkShake *decoratedMilkShake = new MangoMilkShake(baseMilkShake);
cout << "Mango decorated Milk shake \n";
cout << decoratedMilkShake -> Serve() << endl;
cout << decoratedMilkShake -> price() << endl;
    
delete decoratedMilkShake;

decoratedMilkShake = new VanillaMilkShake(baseMilkShake);
cout << "Vanilla decorated Milk shake \n";
cout << decoratedMilkShake -> Serve() << endl;
cout << decoratedMilkShake -> price() << endl;

delete decoratedMilkShake;
delete baseMilkShake;
return 0;
}

But I am wondering: why should the decorator class exist? If I delete it and use only the concrete decorators than everything still works as before. The only downside I see is the fact that I have to use a private pointer to MilkShake in the concrete decorators.

// CPP program to demonstrate
// Decorator pattern
#include <iostream>
#include <string>
using namespace std;
 
// Component
class MilkShake
{
public:
    virtual string Serve() = 0;
    virtual float price() = 0;
};
 
 
// Concrete Component 
class BaseMilkShake : public MilkShake
{
public:
    string Serve()
    {
        return "MilkShake";
    }
 
    float price()
    {
        return 30;
    }
};
 
class MangoMilkShake: public MilkShake
{
private:
    MilkShake *m_MilkShake;
public:
    MangoMilkShake(MilkShake *baseMilkShake): m_MilkShake(baseMilkShake){}
 
    string Serve()
    {
        return m_MilkShake->Serve() + " decorated with Mango ";
    }
    float price()
    {
        return m_MilkShake->price() + 40;
    }
};
 
 
class VanillaMilkShake: public MilkShake
{
private:
    MilkShake *m_MilkShake;
public:
    VanillaMilkShake(MilkShake *baseMilkShake): m_MilkShake(baseMilkShake){}
 
    string Serve()
    {
        return m_MilkShake->Serve() + " decorated with Vanilla ";
    }
    float price()
    {
        return m_MilkShake->price() + 80;
    }
};
 
 
int main()
{
  MilkShake *baseMilkShake = new BaseMilkShake();
  cout << "Basic Milk shake \n";
  cout << baseMilkShake -> Serve() << endl;
  cout << baseMilkShake -> price() << endl;   
 
  MilkShake *decoratedMilkShake = new MangoMilkShake(baseMilkShake);
  cout << "Mango decorated Milk shake \n";
  cout << decoratedMilkShake -> Serve() << endl;
  cout << decoratedMilkShake -> price() << endl;   
     
  delete decoratedMilkShake;
 
  decoratedMilkShake = new VanillaMilkShake(baseMilkShake);
  cout << "Vanilla decorated Milk shake \n";
  cout << decoratedMilkShake -> Serve() << endl;
  cout << decoratedMilkShake -> price() << endl;   
 
 delete decoratedMilkShake;
 delete baseMilkShake;
 return 0;
}