My two cents follows. This is deliberately kind of negative, to counter the excess enthusiasm of the True Believers. The truth is somewhere in the middle, as usual, and there are exceptions to every rule. :^)
1) Everything is a compromise, do not expect perfection. The lack of crossover and single-source location are real virtues which you can't get any other way, but you must give a little on extension, accuracy, and power handling. No free lunch.
2) The deeper and louder the bass, the more air the speaker must move. Cone area times max excursion is the amount of air moved. Anything less than 6.5 inch diameter is never going to give deep full bass - get a sub, or listen to chamber music.
3) Very few fullranges have a flat frequency response; most have either a rising response in the mid-treble (shrill) or hashy treble peaks (harsh) or both. Whizzer cones are the usual culprit, and they are needed on anything 6.5" or greater diameter if you want any treble extension at all. You can see the conflict with 2) ! Look hard for the few exceptions, it's worth it in the end.
4) Most will put out little power above 10-12kHz. Even if they look better on-axis, they are so directional that the power into the room is still very small.
5) Efficient drivers have large, lightweight cones (flimsy) and hence more ragged response. (To be fair, heavy cones can be smooth but are usually also dull and lifeless. No free lunch.)
