There are some problems with current-drive:
The voltage delivered to the speaker varies proportionally to the impedance, so if your speaker/cabinet combination has a large peak at resonance, it will be amplified.
For the same reason, in a multiway system, you will need to linearise the impedance of all sections (a lot of Zobel's and conjugates).
Most loudspeakers are optimised by their manufacturers for voltage drive. Unless you have access to custom-built or OEM speakers, you won't be in a postion to really optimise your design.
I'm not convinced there are many advantages with current-drive.
The most common claim "electric current is that which in a speaker driver effects diaphragm acceleration, which in turn produces sound pressure." is only partially true.
It's the F = B.i.l product that moves the diaphragm, and the induction is not constant, neither the l (length of voice-coil wire immersed in the magnetic field).
For this reason, the effect of counter EMF (and a reasonably low Rdc), is beneficial to the linearisation process of the pressure vs. voltage curve.
Anyway, the current optimisation consists in largely overhung voice-coils, with about 80% of the energy wasted in heat; this is a consequence of the desire to linearise the frequency response of the electrodynamic transducer, which is inherently non-linear.
Voltage translates in voice-coil speed; as a result, the natural response would be a rising one at 6dB/octave, but actually it is the case for the compliance-controlled range, up to a point where it becomes force-controlled and flat, until it reaches the mass-controlled region at -6dB/oct.
Combine this with the cabinet's response and the logical conclusion is that electronic EQ (and/or servo) is the way to go.
Current-drive fixes one aspect of these non-linearities, while enhancing other.