There are true full ranges just because one hasn't experienced one doesn't mean they all require being made into a 3-way.
This statement is false, unless you can show me a driver that really in fact does 20-20Khz and not some made-up stuff like you see on a lot of websites. I've seen some that seem to have 'cracked the nut' but when you dig deeper you find things like a free air resonance that is far too high to allow it to go to 20Hz; things like that.
The other problem you have on the high end is beaminess. If you don't mind having to place your head in a vise in order to get all the highs that's fine. But quite simply, a tweeter can do that job better. If nothing else, a rear-firing or top-firing tweeter is nice to correct the off-axis response so as to maintain tonality when your head isn't in that vise.
But the biggest issue is Doppler Effect distortion. When you have the excursion required to reproduce bass notes, the higher frequencies that are made by the same driver are moving towards you and away from you with those bass notes, causing a pitch bend. If you get the excursion off of the driver, it immediately is lower distortion, resulting in a more transparent reproduction.
So how this works out is less complex music might sound great, such as a solo voice with guitar or a string quartet. But throw some electronia with big bass in it, or a full orchestra playing at a realistic level and 'full range' drivers not supplemented by subs and the like fall right flat on their faces.
IME those drivers with whizzer cones tend to have another issue which is breakups. A breakup can be seen as a peak when you do a pink noise test, but it won't show up as an impedance peak like normal resonances do. So I find the drivers that don't have whizzer cones to have smoother response. PHY for example is pretty good at this (their driver with the best high end seems to be their new 6", which works pretty well in a quarter wave horn cab).
But even if the breakup thing is solved (which can also be solved or at least ameliorated with a crossover) the Doppler Effect thing cannot be escaped. Its very easy to hear how much better any of these drivers get when they don't have the bass to deal with.