First, there is no "perfect" speaker. Far easier to have a perfect anything else in audio as a speaker is a transducer (changes energy from one form into another) and must do so under variable loadings and environments (even a phono cart functions under designed conditions).
So all speakers exhibit distortions, one is simply left to pick their poison(s). Single driver speakers do much right (no crossover distortions, direct loading of the amp, simplier signal path/design, point source imaging, and typically higher efficiency).
One of the first issues to be addressed with single drivers is frequency range. Marketing folks have hyped 20 - 20,000 Hz as a minimum for "full range" performance for decades to the point that now most accept this as fact. Some golden ears and HT lovers would push this range even farther.
Decades ago when amps were all less than 10 watts speaker efficiency was of paramount importance. Horn loading was used and is still the most efficient speaker design known. But bass horns get huge (think of closet to garage in size). So a more limited frequency range was acceptable. One of the often quoted was 80 - 8,000 Hz. Nowadays with powered subs, bigger amps, and better materials we can indeed reproduce 20 - 20,000 Hz and beyond.
Another factor to be addressed is what kinds of music do you listen to. Many musical forms don't require more than say 60 - 15,000 Hz. The room in use is another consideration and bigger is better for deep bass.
However most will agree that midrange (say the 5 octaves from 125 - 4000 Hz) as being the most important. You cannot listen to music and avoid this range. This is the most critical range to "get right". Nearly all multiple driver designs will crossover in this range and therefore add crossover distortion, multiple point sources, phasing mix ups, and voicing from different drivers.
As stated above, literally every driver is more properly described as being limited or extended range. My speakers use a Fostex F200A driver that is rated 30 - 20,000 Hz and I'm very happy with them. The highs (above say 4,000 Hz) do beam, but if you sit near the sweet spot it can actually be a benefit as it limits room interaction. Bass covers everything in unamplified music except for deep organ. And they make for a very purist, simplier is better solution.
