There's a side to defining a arrow that's really confusing. (thankfully the definition of Planck scale leave it all sort of fuzzy).

But consider this. As soon as you make a experiment you must involve your local time keeping, and that one exist, for you and for me too. Doesn't matter there at what scale you define your experiment. I'm free to hypothise scales under Plank scale too, still involving my local time keeping. That's what frames of reference crave, you measuring relative your local definitions, and there your arrow of time (wrist watch) always will exist.

Although, from a purely local definition, not involving comparing between frames of reference, you can reach another definition. And in that one light can't make more than one Planck length, in one Planck time. After that the physics we know 'breaks down'.

And to me, that is a 'Planck clock', ticking one Planck Length, in one Planck time. So it becomes the ultimate, locally definable, 'clock' I can physically imagine. We can't measure at that scale though so it is a theoretical limit.

=

Another point worth mentioning is that sometimes Plank scale constants are used to hypothesize a 'defined universal invariant scale'. That one is true, but as all constants I know of ultimately should be traceable back to ones local definition, then using relativity comparing frames of reference, we reach a definition in where it must be a locally true statement, but 'globally', as in comparing your frame, local time, etc, against another, untrue. That as we then will find time dilations and all sorts of 'contractions/extensions' confusing the issue.

So it is true locally, but not 'globally' in a comparison. Unless you refer to your time and distance measurements as illusions, also invalidating all repeatable experiments. The way to define a repeatable experiment, is to use a local definition, then stipulating that the laws of physics is equivalently valid, locally defined, for/in all frames of reference. As soon as you move from that local definition to comparing your frame of reference to another, you should need to consider time dilations Lorentz contractions, etc.

One can think of it this way. Using a local definition, a Plank length, or Plank time, is just as 'locally equivalent' a Planck length/time at a event horizon, as it is on Earth, for you measuring it locally, being 'on site' so to speak. Locally you should find this definition to hold everywhere. But it won't hold if you instead define it 'globally', comparing your 'Plank length' to what you compute to be 'his Plank length, including relativistic effects over frames of reference, as speed and mass.' (not 'fitting' your results for that other frame through Lorentz transformations)

What it boils down to is whether you accept your measurements to be real, or not? When you talk about a constant you must define it as real, and 'repeatable' (locally measured). And that's the way we built physics.