I always have some difficulty following your arguments. But can you clearly and concisely tell me what is wrong with the following picture below?It doesn't. Firstly, it isn't even the only relational approach to quantum theory (and it isn't much of a relational interpretation at all, but that's less Rovelli's fault than it is the fact that "relative state" was taken and "relativistic quantum mechanics" is not an interpretation but (more or less) the reformulation of quantum theory with the appropriate invariances but without fields or the full-fledged (so-called) second quantization (the term relativistic quantum mechanics is most often used to refer to the modifications of NRQM we find in e.g., the Klein-Gordon equations or that of Dirac).
The Perspectivalist interpretation of Dieks (see e.g. "Quantum Mechanics and Perspectivalism") and his early structuralist-based work on quantum foundations are more in the general intellectual, philosophical, and scientific traditions associated with relationalist approaches and relationalism.
The same is true of the relational quantum interpretation of Dennis Dieks (see e.g., "Objectivity in Perspective: Relationism in the Interpretation of Quantum Mechanics"), or Teller's relational holism ("Relational Holism and Quantum Mechanics"), or Mermin's Ithaca interpretations with its "correlations without correlata" to name a few.
Then there are a slew of related approaches which do not posit any unobservable worlds or hidden variables and their offshoots, such as the modal interpretation or Healey's pragmatist approach or the informational approaches and corresponding interpretations not to mention a slew of others which claim to resolve the issues that RQM likewise claims via more coherent means that also ultimately (I think) fail, such as quantum logics or quantum probability-as-interpretation (i.e., we need to understand that quantum theory describes objective, real systems but that it does so according to non-classical logic or non-classical probability or both and that if we understand QM in these terms than all the problems evaporate).
None of these approaches, in my view, succeeds. In fact, Mermin is now firmly in the QBism camp. But the point is that Rovelli doesn't offer the only interpretation by any stretch of the imagination which claims to explain quantum mechanics without hidden variables or many-worlds or other such additions to the ontology and/or formalism.
Nor, strictly speaking, is it true that he proposes a no-collapse theory. The problem is that several of his claims about RQM seem to be at least in part in contradiction with one another (see e.g., the reply of the authors to Rovelli's response to their earlier work in "A reply to Rovelli's response to our "Assessing Relational Quantum Mechanics''"). RQM, according to Rovelli, is not a "collapse" interpretation because when he and those who follow RQM speak of the collapse of the wavefunction, they don't take the wavefunction as being physically "real" but rather encoding information or probabilities, or more rather it is understood epistemically. Thus the collapse is simply an updating rule as in QBism. But the problem is that RQM claims to be realist in nature. An there is supposed to be an ontology. Simply claiming that any and all systems count as observers and facts relative to the information obtained in interaction and ONLY via these processes doesn't make for a realist interpretation (at least not readily in any coherent manner) because the entirety of the formalism and the mechanisms and the outcomes of measurements and interactions are understood in terms of epistemic processes, relative facts, etc.
This is much like QBism, which is also a no-collapse approach to QM in the same way that RQM is, does not appeal to any hidden variables or many-worlds, and is entirely consistent. Where RQM and QBism differ is that QBism bites the bullet. In wanting to retain, as Rovelli does, the idea of the completeness of quantum theory, eschew hidden variables and worlds, and provide a consistent interpretation, QBists hold that quantum mechanics is about agents. Like Rovelli, probability is emphasized and the quantum states are understood epistemically. Unlike Rovelli and RQM, QBism doesn't try to claim that somehow realism and an ontology emerges magically from interactions and events (that are ill-defined in general in QM, and worse so when one attempts to go beyond using time as a parameter in either the observables or the states themselves). Instead, no ontology is assumed (but Fuchs at least and most of the Boston-based Qbists hold themselves and their interpretation to be realist, like Rovelli).
QBism does run into some of the same problems as RQM. In particular, it is hard to understand how a betting scheme, no matter how consistent it may be, can tell us much about the external, physical world. RQM has the same problem, but refuses to confront it. Instead, at every turn, fundamentally different descriptions of states and physical properties by observers are all supposed to be equally true because...they ought to be? Because that would be a nice world? It's not clear, but other than declaring that by fiat contradictory state assignments and descriptions of the same physical system are not in conflict no matter how clearly they actually are because agents cannot both observe the same contradictions at the same time is honestly little better of explanation for seeming paradoxes than what Bohr and other founders of the so-called Copenhagen interpretation had to offer.
This is simply wrong. I've listed many that do not do so, such as QBism, which takes much more at face value the quantum formalism as does indeed the view of the founders who believed quantum mechanics to be a complete and consistent theory (Bohr and Heisenberg especially, but later e.g., Wigner, Wheeler, etc.). Practically the entire slew of approaches that fall under the so-called informational interpretations and/or statistical interpretations (or ensemble) in the same vein as Ballentine but with the addition of irreducibility and completeness fit your description.
Also, RQM is and has been questioned and found wanting at a basic level of coherence. One can maintain (and people do) that it survives these critiques, but it is hard to see how such built-in, basic contradictions as 1) holding that states in QM are epistemic and evolution and collapse (or equivalents) are to be understood epistemically
and
2) RQM offers a coherent, realist interpretation of QM by claiming that the "relative facts" obtained by observers (which is everything) are objective in some sense and ontological in some sense because truth and facts can be objective as long as we understand that them to be objectively relative to interactions of a formalism that isn't ontological or really even external other than by the kind of fiat Bohr seemed to enjoy with his complementarity.
Reality consists of a set of interaction events. These interaction events are defined through a set of property variables which have values at these interaction events. These property values can usually (but not necessarily) be expressed in a compact way as a set of objects(or fields whatever) doing the interacting. Objects (or fields etc) are only secondarily real in this context... pragmatic ways to encapsulate the information available during these interaction events.
Next...
These interaction events are often correlated. That is the property value of one set imposes some constraints on the likely property value set of another set of interaction events. Quantum Mechanics describes what these probabilistic constraints are and how it can be used to partially predict the properties and their likely values for a target set given the values of another set is known apriori. Wavefunction is a convenient way to encapsulate these relational probabilities in a mathematical structure.
Now does this contradict anything in QM?