Mapman, no, however the match between the speaker and amplifier is paramount. If the speaker has a low impedance at low frequencies, you are going to have to provide the current that making power into that load demands by law (Ohm's Law- no pun intended). The Ohms were always a difficult load! As you have seen, with less difficult loads the requirement for high power at low impedance is less important.
The flip side of the coin has a question- why go where angels fear to tread? IOW **if** the best sound is your goal, it has been shown that higher impedances favor transistors as well as tubes. A transistor amp driving a 16 ohm speaker will sound better (smoother, more detailed, more impact) than it will driving 4 ohms, all other things being equal. So the argument of current, insofar as the goal of 'best sound' is concerned, would seem to be moot.
The flip side of the coin has a question- why go where angels fear to tread? IOW **if** the best sound is your goal, it has been shown that higher impedances favor transistors as well as tubes. A transistor amp driving a 16 ohm speaker will sound better (smoother, more detailed, more impact) than it will driving 4 ohms, all other things being equal. So the argument of current, insofar as the goal of 'best sound' is concerned, would seem to be moot.