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Low Frequency Quasi-Periodic Oscillations or LF QPOs are ubiquitous in BH X-ray binaries and provide strong constraints on the accretion-ejection processes. Although several models have been proposed so far, none has been proven to reproduce all observational constraints and no consensus has emerged yet. We make the conjecture that disks are threaded by a large scale vertical magnetic field that splits it into two radial zones. In the inner Jet Emitting Disk (JED), a near equipartition field allows to drive powerful self-collimated jets, while beyond a transition radius, the disk magnetization is too low and a Standard Accretion Disk (SAD) is settled. In a series of papers, this hybrid JED-SAD disk configuration has been shown to successfully reproduce most multi-wavelength (radio and X-rays) observations, as well as the concurrence with the LFQPOs for the archetypal source GX 339-4. We first analyze the main QPO scenarios provided in the literature: 1) a specific process occurring at the transition radius, 2) the accretion-ejection instability and 3) the solid-body Lense-Thirring disk precession. We recall their main assumptions and shed light on some severe theoretical issues that question the capability to reproduce LF QPOs. We then argue that none of these models could be operating under the JED-SAD physical conditions. We finally propose an alternative scenario where LF QPOs would be the disk response to an instability triggered in the jets, near a magnetic recollimation zone. Such a situation could account for most Type-C QPO phenomenology and is consistent with the global behavior of black hole binaries. The calculation of this non-destructive jet instability remains however to be done. If the existence of this instability is numerically confirmed, then it could also naturally account for the jet wobbling phenomenology seen in various accreting sources.