I've heard a few systems with a single driver where I thought the sound was quite good, overall, and particularly good in certain aspects. The single driver systems I liked were the Charney Audio Companion (particularly with the AER driver) and the Voxativ Ampeggio and Songer Audio S1. Most of the others I heard had too rough and peaky upper midrange colorations; I did not mind as much the lack of really deep bass. I agree with those above who say that using the full-range driver as a wide range driver in a multi-way system is a better application of such drivers. With the right wide-range driver, the crossover points can be set low enough and high enough to be out of the range where the ear is most sensitive to crossover anomalies. Also, wide range drivers allow for the use of simpler crossovers with shallower slopes.
I've heard a number of successful custom builds using such drivers in multi-way system. Many are custom-built systems using some fairly exotic Western Electric and Jensen drivers (like the field coil M 10 and M 18 drivers). Among successful modern multi-ways are the two-way are the Cube Audio Nenuphar Basis (to me, MUCH better than their single driver systems), and the Songer Audio S2. I've heard really nice horn-based systems where gigantic horns were used to allow a very low crossover such that the compression midrange was crossed over to the bass driver at 150 hz and the crossover to the tweeter was around 8,000 hz. Even the best of these systems have compromises, of course, mostly in that they don't go extremely deep. But, the speed, purity, liveliness and vivid quality of wide-range drivers used correctly makes such compromises worthwhile.