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Seems like a neat line of consideration, though perhaps not too compelling as an overall assessment so much as an exploration into a thought-experiment.
For example of an obvious limitation, let's say that Alice wants to figure out if she's living in a simulation, so she goes about trying to establish the complexity of the universe, perhaps working to establish higher values for the lower-bound to better evidence the proposition that the universe isn't a simulation. While it might seem like Alice could seek to arbitrarily raise that bound, Alice herself would seem to be finite in complexity -- and so if we consider Alice as a finite-state-machine, then the lower-bound of a full solution to tricking her would be of finite-complexity. And even a requirement for that much complexity would still rely on an assumption that Alice's mind is perfect and outside of any mechanic that might frustrate such an analysis.
This is, an analysis based on the universe's total complexity might make more sense if someone wanted to assume a specific form of the universe. However, if someone wants to prove that they're not a brain-in-a-jar, then they'd seem to have more trouble establishing a significant lower-bound.
Beyond that, the idea of a straight simulation -- like in a straight physical program run on a modern-day electronic computer -- would seem like a naive background assumption. Neat as a starting place for a thought-experiment, though perhaps not so useful as an actual mode of analysis.
All of that said, thought-experiments like this might help motivate conceptions of what kinds of simulations might be more plausible. Because while the concept of ANY simulation would be pretty general, arguments like this might be applied to assess the plausibility of specific types of simulations. For example, it'd seem reasonable enough to say that the universe's complexity seems to be of sufficient vastness that the universe probably isn't a simulation maintained for the specific purpose of calculating 1+1=2.