Literal class with std::string only works with template specialization?

The following definition is not allowed by my compiler as std::string has a non trivial destructor (makes sense that teststr can't have a trivial dtor when a member doesn't):

class teststr
{
private:
    std::string _m;
public:
    constexpr teststr(std::string value) : _m(value) {};

    constexpr std::string m() const { return _m; }
    void m(std::string value) { _m = value; }
};

However, the following equivalent (to the best of my knowledge) definition of teststr is allowed:

template<typename T>
class test
{
private:
    T _m;
public:
    constexpr test(T value) : _m(value) {};

    constexpr T m() const { return _m; }
    void m(T value) { _m = value; }
};

typedef test<std::string> teststr;

What is it about templating the type that makes this definition allowed?