Planck time doesn’t appear to be arbitrary, but a feature of our universe, hence the shortest measurable unit of time. It’s length in seconds is arbitrary because seconds are arbitrary. And seconds are arbitrary because the only non-arbitrary unit of time we have found so far is too unwieldy to use for anything but scientific purposes, and it’s very unwieldy for many of those.
Planck time doesn’t appear to be arbitrary, but a feature of our universe, hence the shortest measurable unit of time. It’s length in seconds is arbitrary because seconds are arbitrary. And seconds are arbitrary because the only non-arbitrary unit of time we have found so far is too unwieldy to use for anything but scientific purposes, and it’s very unwieldy for many of those.