Unless I'm missing something, Shalizi usually makes more sense than this.

1) Measurements use work (or at least erasure in preparation for the next measurement uses work). They do not simply magically reduce our uncertainty without thermodynamic cost. Even if you measure and never erase, the measuring system must be in a prepared state, cannot be used again, and still produces entropy if you are not operating at absolute zero / infinite precision, which you can't do (third law of thermodynamics).

2) Because we are not logically omniscient, we lose information we already have as the result of not being willing to expend the computational cost of following every atom. Liouville's Theorem preserves a volume of probability but it can get awfully squiggly, so if you preserve a simple boundary around your uncertainty, it gets larger.

3) Quantum universes branch both ways and create new uncertainty in their branched agents.

Done.