Low-frequency quasi-periodic oscillations, or LFQPOs, are ubiquitous in black hole X-ray binaries and provide strong constraints on the accretion-ejection processes. Although several models have been proposed, none has been proven to reproduce all observational constraints, and no consensus has emerged so far. We make the conjecture that disks in binaries 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 driving 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 multiwavelength (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 of reproducing LFQPOs. We then argue that none of these models can be operating under JED-SAD physical conditions. We finally propose an alternative scenario according to which LFQPOs are the disk response to an instability triggered in the jets near a magnetic recollimation zone. This situation can account for most of the type C QPO phenomenology and is consistent with the global behavior of black hole binaries. This nondestructive jet instability remains to be calculated, however. If this instability is numerically confirmed, then it might also naturally account for the jet wobbling phenomenology seen in various accreting sources such as compact objets and young forming stars.