This is a very philosophical / meta-physical discussion of quantum mechanics, and not in line with our modern understanding of the measurement process. For example, there really is no sudden wave function collapse in quantum mechanics, as every measurement process can be described as a purely quantum-mechanical process that produces an apparent "collapse" of a wave function through entanglement and decoherence. There's nothing magical or abrupt about it, today we can even perform quantum measurements that precisely control the amount of decoherence that is introduced to a system (see e.g. some of Irfan Siddiqi's seminal quantum feedback experements like
https://www.nature.com/articles/nature11505, or the earlier work done in Serge Haroche's group). Taking aside the philosophical problems that people have with "pure" quantum mechanics (i.e. an interpretation that does away with the second postulate of wave function collapse) it perfectly describes our experimental results.
The largest problem with wave function collapse (which the author only briefly skims) is that you need a way to explain how it works: Basically when the wavefunction collapses we go from a fully reversible, deterministic quantum system to an irreversible, stochastic system. At which scale is this supposed to happen? Let's say one day we can build huge quantum computers (think billions or trillions of qubits) that we can perfectly control. We could then prepare a single qubit in a superposition state. We can entangle this qubit with the other qubits (the measurement system) and manipulate the state of the measurement system using a deterministic but highly chaotic control program. If we'd then measure the state of the single qubit (e.g. by preparing many identical systems and performing quantum state tomography) we'd find that the wave function has collapsed, i.e. there is no more coherence between the two qubit states. Now, after entangling the qubit and evolving the large system we could just reverse its deterministic evolution (as we have perfect control over it) and bring it back to the state it was in directly after entangling it with the qubit. If we then perform quantum state tomography of the qubit we should see that the coherence is back. Now, if we believe that wave function collapse is a phenomenon that occurs independently and not as an effect of the evolution of the large quantum system, we would expect to observe a loss of coherence in the qubit even after perfectly reversing the state of the large quantum system. The question is then of course: At which scale does this happen, and what is the physical theory that governs this behavior? Are one billion qubits enough to produce it? One quadrillion? To my knowledge, no one came up with even an idea of how to describe this. If someone finds a good theory for describing wave function collapse I'll consider it as valid theory, until then I'll stick with the "many worlds" interpretation, though I'd really prefer calling it "plain" quantum mechanics instead.