The [amplitude samples] -> [frequencies+amplitudes] transform has finite precision. First reason for that - the signal component sine waves do not last indefinitely and do not have precisely constant amplitudes - necessary conditions for obtaining perfect readings of their exact frequencies and amplitudes.
Furthermore, the transform is done via a finite window, usually in the range of 512 to 2048 samples depending on algorithm, which may further reduce the precision. Making the window wider doesn't usually make much sense because the characteristics of the audio signal are bound to change over that duration.
So, even a perfect non-decaying sine wave (which are very rare in "non-boring" music) in general case could only be captured as a distribution over the frequencies that the finite-window transform, figuratively speaking, is trained to recognize. The real-world abruptly starting and slowly decaying sine waves are even more difficult to recognize precisely.
For example, instead of returning correctly one reading of a wave with 100% of energy at 7500 Hz, a transform may return something like 10% at 7200 Hz, 40% at 7400 Hz, 40% at 7600 Hz, and 10% at 7800 Hz.
In the example above, if the crossover frequency happens to be 7500 Hz, the transform will end up yielding four pretty close frequencies which, when being reproduced by two transducers, will be canceling and amplifying each other depending on the phase shift and time.
So, a good digital crossover must be smarter than just an analog filter brought into digital domain. It needs to take into account neuro-physiology of human hearing. Just like MP3 and AAC encoders do.
For instance, in the example above, a good digital crossover would "figure out" what's going on and maybe shift the apparent frequencies a little bit so that they all could be first aggregated and then reproduced by just one of the transducers.
Still, no matter how smart the digital crossover is, it will never be technically ideal. Yet given enough precision and sample rate of the digitization, as well as enough RAM and processing power, I believe it can be made transparent enough so that the fusion of the several transducers will appear perfect to most human ears.