What do you mean by "pursue"? If you mean trying to produce a full-fledged theory of quantum gravity that can be "directly added" to the standard model, it's most likely not worth to "pursue". See for instance, this "proof".

But often, we can use theories which are actually inconsistent, but can give some meaningful results that can be used to test more complete theories. An obvious example that comes to my mind is Supergravity.

Similarly, trying to quantise gravity like any other force can actually yield meaningful results, making it certainly worthwhile to pursue. For instance, one may calculate graviton-graviton scattering amplitudes at the tree level, and see if the same predicted by string theory reduces to this when one takes the limit as \(\alpha'\to0\) - the exact factor by which one multiplies the stringy prediction by to get the field theory prediction is:

\( \frac{{\Gamma \left( {1 + \frac{{\alpha '}}{4}s} \right)\Gamma \left( {1 + \frac{{\alpha '}}{4}t} \right)\Gamma \left( {1 + \frac{{\alpha '}}{4}u} \right)}}{{\Gamma \left( {1 - \frac{{\alpha '}}{4}s} \right)\Gamma \left( {1 - \frac{{\alpha '}}{4}t} \right)\Gamma \left( {1 - \frac{{\alpha '}}{4}u} \right)}}\)

Take the field-theoretic limit and this approaches 1 (obviously) with no dependence on *s*, *t*, or *u*. See Mohaupt's lecture notes on string theory for more details.

So to answer your question, yes it is worthwhile, but not as a theory of quantum gravity on its own right.