quantum gravity -- why not ?

[Widdekind]

If, by applying the Correspondence Principle, to the Classical Relativistic 4-vector equation [math]\vec{p} \circ \vec{p} = m^2[/math] yields the Klein-Gordon equation [math]\left( \partial_t^2 - \partial_x^2 \right) \Psi = m^2 \Psi[/math]; then, why not simply extend the 4-dot product, from Minkowskian flat space [math]\vec{p} \circ \vec{p} \equiv p^{\mu} p^{\nu} \eta_{\mu \nu}[/math], to curved space, via the GR metric [math]\eta_{\mu \nu} \rightarrow g_{\mu \nu}[/math], i.e., [math]\vec{p} \circ \vec{p} \equiv p^{\mu} p^{\nu} g_{\mu \nu}[/math] ? Likewise, for purposes of computing the metric tensor, from the wave-functions, via the Stress-Energy Tensor, one could simply treat the quantum wave-functions as "smeared out particles" (could one quote "the big names, in the big chairs", and simply say, "shut up & calculate" ?), and calculate the SET with terms vaguely like [math]T_{\mu \nu} = \Psi^{*} p_{\mu} p_{\nu} \Psi[/math] ??