A compilation error occurs in your code because the compiler does not know that T has a method named Add that receives one string parameter.
I thought that generic types in Delphi are simply inserted into a generic function, so it will only be an error if it is used with a type that does not have an Add (string) method.
If you use Smalltalk or C ++ templates, your guess would be accurate. However, generics do not match the patterns. For generics, you need to apply a restriction to the type parameter. The restriction should tell the compiler which properties of T should have.
For example, you can restrict T to be obtained from a class that has a suitable Add method. Or you can restrict T to implement the interface using the appropriate Add method.
Documentation link for general Delphi restrictions: http://docwiki.embarcadero.com/RADStudio/en/Constraints_in_Generics
The general restrictions that can be applied are quite limited, which is a bit of a shame. For example, I would like to keep the type in order to have certain mathematical operators. For example, I would like to be able to restrict the type, for example, the + and - operators. However, there are pros and cons for both generics and templates, and therefore I agree that these restrictions are the result of a sound design decision by the Delphi developers.