String theory, besides Phenomenological problems such as supersymmetry and extra dimensions, is far from a theory deserves to be called a theory of everything!
it doesn't explain quantum gravity as you said because QG has a number of conceptual problems such as "the problem of background independence", "the problem of time", etc that string theory doesnt' have any answer to them. for example the current consensus in fundamental physics community is that if a theory of QG exists, it must be background independent so if QG be a QFT, one must define a generally covariant QFT without background which is a concept that is not properly formulated (I guess there are several attempts in LQG community) because it is very different from conventional QFT's and there is no background indepedndent formulation of string theory and some attemps to construct such a theory using simpler models such as topological strings theory and topological M-theory hasn't been so successful! there was a hope in the last years started at mid 80's that when one quantized string theory in the spectrum of resulting theory, there are particles behave like a spin 2 particle like graviton and some gauge fields like Yang-Mills and in this sense string theory is a theory of QG which seems more like a joke! these are outside problems that string theory must face beside some inside problems of the string theory itself! for example :
1) the problem of number of vacuum solutions of M-Theory;
2) one doesn't not know what is the classical theory of gravity in string theory because in classical sting theory, one doesn't have gravity at all! like YM theories that approximated by Nonlinear Born-Infeld fields
3) the dynamics of second quantized string theory (string fields) hasn't been understood except some simple ones such as Witten cubic open string field theory
and ...
so it is far from a complete theory if it be a well-defined theory at all!