It's like this with so much media, it drives me crazy. For instance, in the country I'm currently in there is no way to legally watch a lot of movies - not because of censorship or anything, they are simply not distributed, even on google-play, amazon etc. No choice but it use torrent. Why?
No, Planck units have no intrinsic physical significance. They're just convenient to work in because they set the numeric values of several different physical constants to 1. The planck distance also happens to be roughly the length scale at which we expect quantum-gravitational effects to become significant, but roughly here means within a few orders of magnitude.
> Hmm, so doesn't the fact that this particular value makes the math simplified not also imply some kind of meaning?
No. There are plenty of other sets of constants you can choose to set to 1, inducing other length scales. Only dimensionless constants have physical meaning in isolation; dimensioned quantities are meaningful only with respect to each other.
Fine structure constant, famous alpha ~1/137. It also means that you could multiply or divide what we know as Plank length and it still would be a "valid" unit to be a minimum length entity