We have no reason to believe that the Planck length actually has any physical significance. It is just a way to get something of a certain order of magnitude fr

We have no reason to believe that the Planck length actually has any physical significance. It is just a way to get something of a certain order of magnitude from physical constants. The quantization in quantum mechanics arises from constraints on the physical systems being studied. There are no constraints that would lead to length itself being quantized. You can get wavelength quantization for bound particles, but that's just for that particle, not for space in general.