I think a better counter is the question "Is there a meaningful difference between binary discretization and Planck units? Aren't those discrete/indivisible as well?"

That's not really a good counter - Planck units are not a discretization. Space-time is continuous in all quantum models, two objects can very well be 6.75 Planck lengths away from each other. The math of QM or QFT actually doesn't work on a discretized spacetime, people have tried.