It seems to me that the UV divergences in a quantum theory of gravity could be canceled by just requiring the distance between any two points be finite. I know loop quantum gravity basically addresses this through the quantization of area and volume, but you don't even need loop quantum gravity to do this. Not to mention, I hear there there are a lot of problems when you try to create a perturbative theory to LQC. If you postulate the distance between two points is finite, I think you can create a quantum theory of gravity devoid of UV divergences. What are the problems of doing this?