So, the equations for general relativity are as follows: $$G (mu, nu) = ĸ T (mu,nu)$$ I was told, that since energy, momentum and other observables are quantum then the stress-energy tensor $T$ is quantum, and therefore the Einstein tensor $G$ must be adapted to it. However, what if we used expected values $\langle T\rangle$ to make the stress-energy tensor "classical" which makes quantum gravity "unnecessary". How would this lead to any problems, and why haven't we tried it?