My impression is that many audio designers don't fully understand the amplifier--speaker interface. Especially they don't fully understand "damping" and they are not aware that while there is feedback, it is local degenerative feedback in the speaker driver itself.
Damping is defined by the total terminating impedance the voice coil sees. Most of that is its own static impedance, described by its DC resistance Re plus some static semi-inductance. The amp's output impedance comes on top of that and is pretty much irrelevant, even in an active speaker, because Re is orders of magnitude greater. With series elements in between in case of passive crossovers, it's even more irrelevant. "Damping factor" is a red herring and no serious designer would ever use that term, it was invented for marketing only.
The above describes the standard case where the amp is designed as a voltage source with low and stable output impedance. The topology of the amp does not matter for this.
Amplifiers can be designed with arbitrary output impedance, though. For a practical system, the real part of the impedance can even be negative, but not more than -Re for obvious stability reasons. At the other end there are no restrictions, the output impedance may reach positive infinity, representing a true current source.
Now what does that imply for the damping and the feedback it establishes?
The current drive case is easy to explain. The driver is operated in pure force-controlled mode, the current creates a force F=BL*i that is impressed. The microphonic voltage (aka "back-EMF", a term that shouldn't be used as it only creates confusion) can develop freely and simply goes into the voids. Think of it like a signal generator in series, the current source doesn't care, it still injects the current demanded by the amp's input signal. The only damping present is the mechanical damping of the driver in the given build. At resonance, only little current is needed to exite the movement which means the current profile must have a proper shaping (EQ) to get a flat frequency response. This technique is fraught with problems because of the instablilities, at least for standard drivers in standard enclosures that are to be operated at their resonance frequency and have little mechanical damping. Above resonance, or if resonance is well controlled mechanically for example with resistive air load in horn designs, it is feasible though and actually has some significant benefits.
Current drive means no local feedback in the driver, as the microphonic voltage has zero effect on the output, the driver is free to move, only steered by the force generated by the impressed current.
Let's look at the opposite corner case, terminating the voice coil with very close to zero effective impedance (output impedance of amp = -Re + some small safety marging, lets assume to use 99% of -Re). The voltage of a moving voice coil always is E = i*Re + k*dx/dt, in words, the sum of the voltage drop along the static impedance plus the microphonic voltage which is proportional to voice coil velocity (1st derivate of the voice coil displacement x). Because the effective Re now is only 1% of the Rdc of the driver, the i*Re term is quite insignificant. The amplifier now controls the velocity of the driver directly. When the microphonic voltage produced by the motion does not match the required voltage as per amp's input signal, even a small voltage difference produces a huge correction current because the effective Re is so small. This a true feedback mechanism, the driver is operating in velocity-controlled mode by the feedback. Because sound pressure is proportional to cone acceleration (below the point the cone starts beaming), the input signal must be EQ'd to a falling 20dB/decade slope vs frequency to get the required velocity profile.
Again, full feedback of this kind isn't practical for many reasons, the most important one being the static impedance not being stable, the DC resistance has thermal drift and the inductive part is instable, current and position dependent, etc. On top of that, the sensor itself is not linear, the microphonic voltage starts to drop when the VC starts to leave the gap, leading to a nasty overshoot reaction (the feedback "thinks" it must correct for an apparantly too low velocity and impresses counteracting current until the senses voltage matches the input, but then the actual velocity is too high).
Which leaves us with usable ranges for the output impedance somewhere in between these extremes. It can be found empirically that for a given driver in a given enclosure design there is a terminating impedance profile vs frequency that gives the best results overall with the lowest distortion and a stable large-signal behavior, notably a clean and quick overdrive recovery, in most cases this impedance does *not* result in zero output impedance of the amplifier. Therefore, it often is a good idea to have some series elements in the path to the driver even in active systems with standard voltage amplifiers, and it is good for noise as well. This is also a reason why a passive design may actually measure and sound better than its active replica with all drivers terminated with zero impedance.
Special acoustic loadings need special treatments wrt to terminating impedance, for example a ported box needs a properly adjusted mechanical damping of the Helmholtz resonator to make it effective. Notably too high damping of the driver (brickwall behavior) is a bad thing, make the port Q too high and its output contribution too narrow-band. Too low damping isn't good eiher, making the port ineffective. Closed boxes or open dipoles typically work best when the excursion shows close to critical damping in its step response which means the driver settles fast from its own error signal, notably after an overdrive event. Too small damping results in ringing at the resonance whenever the cone is exited by an external signal (including its own errors), EQing the input signal doesn't help here because the error develops after that. This is one of the reasons why current drive doesn't work nice at resonance.