Their sensitivity of generally around the 86dB mark makes them rather inefficient and therefore, at least in theory, not a good match for many lower powered tube amps, or any amps below 100wpc. Their frequency range is simply inferior to most high-end speakers since they don't go below 40 Hz.Disclaimer - I have Spendors, not Harbeths. But they are from the same BBC lineage.
Try this perspective; the vast majority of natural musical sounds we hear are in the midrange, and they are not super loud. The fundamentals of the human voice primarily reside in frequency range of roughly 100 Hz to not much more than 1,000 Hz. Very few instruments have fundamentals above 4,000 or 5,000 Hz.
Everything above that is pretty much harmonics. These are certainly important, but if you don't have the critical midrange right, then all the bass, upper highs and extra volume won't fix the lack of naturalness.
Speakers are like any other product. Think of the old debates between car owners. Some people like the power and acceleration of an old school muscle car and others are more taken by the nimble suspension of a road-tuned sports car. Each group likes what they like and no amount of rationalization from the other side is going to change their minds.
The only thing you can do is listen to a set of Harbeths and see what they do for you. You may be enchanted, and then again, you may not.