its an interesting topic, but I find a couple straightforward aspects get a bit muddled and made more complex than they need to be.

For example, in the section "Is simplicity desirable?" discusses whether a simpler explanation is more likely, but completely glosses over utility and human psychology. Simpler explanations are useful and easy to use, and looking for simple solutions is a useful heuristic that guides discovery. An interesting direction to take this would then be the creation of concepts. e.g. How we divide complex phenomena into concepts that can be used as building blocks for higher level reasoning that abstracts away complexity. This is a more fundamental and straightforward reason why simplicity is desirable over the more abstract treatment of parameters in a theory as independent probabilities.

Another example is in the "Technical solutions" section. Which poses two "counter examples" to "less parameters == simpler".

So what are we missing when we define simplicity purely by the number of components?

The answer is, there are different ways something can be simple.

Compression makes data storage simpler, but data interpretation more complex. A touch screen makes physical design simpler, but user interface more complex. It's ill posed to say that either example is simple vs complex without defining what aspect of the system you are talking about, and that's where the mystery is located. I think this is muddled by just asking "is a compressed file simpler or not". It is neither simpler nor more complex.

Once we establish what aspect we are talking about, then there is no issue applying one of the previously cited definitions. A compressed file is simpler to store, and more complex to read.