Does the notion of blurriness of lightcone appear in any theory of quantum gravity?

In the above diagram, black lines are $x=pm t$ and the highlighted space is what I meant by the blurriness of the lightcone.

Personally I have 2 arguments and both seems to suggest there shouldn’t be any blurriness.

• In GR regime the light cones are there not because of some property of massless particles but because
  of the intrinsic nature of the geometry of spacetime.
• Though in Quantum mechanics the particle can’t be localized, even the
  $hat{x}$ eigenvectors spread over time. In QFT we use distribution
  function to force $[hat{O}(x),hat{O}(y)]=0$ for $(x-y)^2<0$, signature is $(+,-,-,-)$. But such distribution are ill-behaved at very small distance