Current drive amplifiers outputs current instead of voltage. But they are almost non existent in audio world. In example First Watt F1 and F2 amplifiers could be called current drive amplifier. They have output impedance about 10 times or more higher than speakers impedance. So its fare enough to call it current drive amplifiers. And people like them. Yes they are not for everyone, because in box speakers and passive systems they can do more harm than benefit for the sound. But for active open baffle speakers they are perfect. The advantage of current drive amplifiers is that the speaker connected to them produces less high order harmonics. Which are detrimental for the sound quality. Sometimes low order harmonics can be higher a little bit with current drive, but it depends on many factors. So THD measurement can be about the same for voltage and current drives, but the sound is not. And with less high order harmonics it is a lot more pleasant, more air in the sound. It is just more lifelike and clean. This is part of a reason why tube amplifiers sound pleasant. Tube amplifiers acts like something in between voltage and current drive because of its relatively high output impedance. In Pic.1 voltage drive THD is better with 0,77% vs 0,89% for Pic.2 current drive, but the spectrum is a lot cleaner for current drive! And also low order harmonics can be masked, because of the masking effect of human hearing.  Both voltage drive and current drive can have advantages for some particular cases. It depends on the driver type, speaker type and many other factors. But for my case current drive is a better option. And interestingly enough that some current drive drawbacks can become advantages in open baffle arrangement. Like boosted low end at the resonant frequency.

More about current drive you can read here https://www.current-drive.info. And this older paper from professor M.O.J Hawksword and P.G.L. Mills.