I don't think current physics works below the Planck length. There aren't all that many infinities in physics in general, and where the do pop up, they're problematic.

Whereas in mathematics, infinities are a rich field of research, which goes way beyond anything that could ever be physical.

Besides, the tension doesn't exist, because whether or not spacetime is infinitely subdividable, going a certain distance takes a certain time, and going a fraction of a distance takes a fraction of time. The two series will converge in both the discrete and the continuous scenario.