The word "signaling" necessarily implies the transfer of classical information (because of the no-cloning theorem) and that in turn implies some model of the transition between quantum and classical. Whether that transition is (meta)physically real (i.e. collapse) or just an arbitrary threshold applied to a continuous process (decoherence) doesn't matter. What matters is that FTL leads to a logical contradiction with respect to the characterization of the state with respect to whatever model you choose to apply. The underlying metaphysical reality is irrelevant.
Eh, that model might still allow you to probabilistically send information back in time, in a way that saves the universe from an outright causal paradox (a weird "chronology-protection" principle of sorts). You can't send your patent back in time and generate prior art that destroys it, but you can end up with a 50:50 probability of doing so, and that description is logically self-consistent. Probability is still "classical".
All communication is probabilistic. There is no such thing as a noiseless communications channel. But per Claude Shannon you can always tilt the odds in your favor as much as you like given enough time and energy.
Pick some example of a "causal paradox" of the sort that might introduced by FTL signaling. If the underlying system is a quantum one (hence with continuous amplitudes, albeit the reasoning also extends to simple probabilities) no logical paradox actually arises because the underlying values are continuous. This would imply that there's no difference between that and a CTC.
Of course larger-scale physics appears classical to us but that's a consequence of quantum decoherence and ultimately of the "law" of increasing entropy (2nd law of thermodynamics). Which is just as much of an obstacle to classical CTC's.