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Philipp notes that the quantum reconstruction program (QRP) is looking for “physical” and “conceptual” principles that can be used to derive the Hilbert space formalism of quantum mechanics (QM). As it turns out, there is an answer in QRP if you (re)spatialize the notion of measurement, as we explain in our book, "Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit" Oxford UP (2024). Let me summarize it here. QRP has successfully rendered QM a principle theory and its empirically discovered fact is called Information Invariance & Continuity (Brukner & Zeilinger 2009; other starting points are used of course). If you spatialize the notion of measurement, Information Invariance & Continuity entails that everyone measures the same value for Planck's constant h, regardless of their relative spatial orientations or locations (let me call that the "Planck postulate"). Since h is a constant of Nature according to Planck's radiation law, the relativity principle says it must be the same in all inertial reference frames. And, since inertial reference frames are related by relative orientations or locations in space (rotations or translations), the relativity principle tells us the Planck postulate must obtain, whence the finite-dimensional Hilbert space of QM. That’s every bit as “physical” and “conceptual” as the light postulate as justified by the relativity principle for special relativity. Consequently, I don’t see how anyone can deny the success of QRP.