One thing that should be made clear is that "Full Range" is a bit of misnomer for the average listener of moderate income and room size. Very, very, few speakers of any driver design actually cover 20Hz-20kHz(-3dB) accurately. Very few do 30Hz(-3dB) accurately. Those that do are usually very big, very heavy, and very expensive.
Fullrange single drivers have their advantages and limitations. I think the first sonic benefit that most fans, like myself, will tout is their musical "coherence". What does that mean? That the entire musical spectrum seems to emanate from one, seamless, sonic tapestry without any inconsistencies. It's very hard to describe in words, but once you hear it, it is very hard to accept anything else.
Why do they seem more "coherent" to some people than other multi-driver designs? I think most of us, like Macrojack, will cite no, or 1st order, crossovers and no need to transition between differing drivers at the crucial midrange frequencies where the ear is most sensitive to anomalies. Seamless transition between drivers of different size and construction materials is not easily done and fairly rare.
The downsides - like all speakers, bass. There are only three ways to deep, accurate, bass; 1) large driver surface area, 2) long driver excursion, 2) big cabinet. Usually, two of the three are necessary unless lots of power is needed.
And single drivers generally need really large cabinets to go deep with any authority. Even then, they won't move the same amount of air as good multi-driver designs. But, well-executed designs will have very fast and clean bass, which can be supplemented by good subwoofers.
Which brings us back to - is that really a single driver system? No, not in the strictest sense. But, single driver advocates are primarily concerned with a driver covering the most critical section of the frequency range in it's entirety - the full midrange (400Hz-6kHz). Most single driver proponents would even like to push that out to 8kHz-10kHz.
BTW, Tannoys aren't single drivers, they are coaxials with a center-mounted tweeter. But, their 12' or 15" driver does cover the entire critical range anyway. And they are pretty awesome when properly implemented in the right cabinet.