How do I make all child-classes inherit all constructors in the parent class, automatically?

 class Animal{
     public Animal(){... blah blah…}
     public Animal(string name){ ... blah blah…}
 }
 class Cat:Animal{
     public Cat(string name):base(name){}
 }
 class Dog:Animal{
     public Dog(string name):base(name){}
 }

…

 Animal a=new Cat(“cat”);

…

This seems like a real pain, if I have a bunch of different constructors and a bunch of child-classes. Why aren't those completely EMPTY Cat & Dog constructors, that ONLY call the base class constructor, automatically IMPLIED, unless specified otherwise? It seems like, only the default constructor, without any parameters, is automatically inherited like this (unless specified otherwise).

Main Question: Is there some syntax to tell the compiler do this?

(If I don't define that Cat constructor manually, the compiler generates this error: ‘Cat does not contain a constructor that takes 1 argument’ on the line: Animal a=new Cat(“cat”); )

I know a lot of thought went into c#, so perhaps there is something I am not considering, that would make this a bad idea?