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Is there any actual justification for viewing spacetime as being discrete, with unit 1 Planck length/time? As far as I'm aware, the Planck length is just a length you get when you multiply a load of constants together.

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You're absolutely right. The plank time is just a time such that events that happen in sufficiently smaller time intervals probably need new physics to describe. This is comparable to how very fast moving objects needed more than Newtonian physics to describe, namely relativity, or how very small objects needed quantum mechanics. It may be that that new physics is discrete, but at this point we have no idea.

>a time such that events that happen in sufficiently smaller time intervals probably need new physics to describe //

Physically¹ events happen instantaneously we just can't tell at which precise instant they happen. This is true even with quantised time.

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¹ Perhaps that should say "in the mathematical model of the physical universe we base our science on".

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