Some of the disadvantages would be
A disadvantage: template errors are only detected by the compiler when the template is instantiated. Sometimes, errors in the methods of templates are only detected when the member method is instantiated, regardless if the rest of the template is instantiated.
If I have an error in a method, of a template class, that only one function references, but other code uses the template without that method, the compiler will not generate an error until the erroneous method is instantiated.