More to the point, a ferrite bead won't do anything at 3A, due to saturation.
Is it still the case if I'm using the FB in picture which is rated up to 12A@85C?
That's strictly the thermal rating, for whatever (usually 40C) temp rise -- it has no bearing on saturation current.
Murata does not provide bias data for this part (or most any of them, sadly; at least not in an accessible format, maybe their "bias tee" tool contains such data but good luck with that.
The nearest Laird equivalent is probably HI1206T500R-10, although rated only 6A. It shows about, hm not 50, closer to 45 ohms at 100MHz, but whatever; that's at zero bias. At 1A, it's down to about 32 ohms, so, nearly -30% impedance -- a typical threshold to consider "saturated".
Lower impedance beads do tend to retain impedance better, and it's noteworthy that impedance is still droppping over the 3, 4, 5A range; it doesn't saturate suddenly, but is roughly inverse proportional to bias. (Which makes sense, as the construction is probably a single wire link through the middle of a ferrite block: the inner radius closest to the wire saturates first, and more further out as bias goes up.) But two things remain true:
1. you don't get the same attenuation under load as at no-load, it's inconsistent so you must design around both worst-case extremes;
2. if you aren't aware of this effect, you're probably not getting the value you were expecting!
Both circumstances can lead to frequency responses wildly different than expected. I'm a big fan of avoiding surprises, and this effect is poorly documented, so I repeat it at every opportunity.
The ramp rate model is just something I got from reddit which in hindsight maybe wasn't the best source of information. However looking at the capacitor current formula I see that the rise time is part of it: \$I = C\frac{dV}{dt}\$
And indeed if I increase the 1us rise time to 1ms in the above simulation the current level drops to mA level at the damping resistor. Or am I completely off base?
Indeed. However, you can try it for a say 10ns rise into a 0.6uH inductor and the rest of the circuit, modeling the hot-plugging of [an inductive] cable 1m long.
Even more interesting is when the filter capacitors are high-K ceramic, which similarly saturate (C decreased) under V bias. The resulting peak overshoot can be several times the supply!
Tim