Thank you all for your contributions to my question.
Using steep filter certainly will solve some problems, but the delay will still be there between the bass, midrange and tweeter and this will produce unwanted lobing effects to the sound.
I know this because I have done experiments with it.
In a two-way horn system, very much like a Belle Klipsch. The bass unit was working up to about 800 Hz and from there it used a Pioneer horn, the PD/PH-50, which worked from 800 to about 20 kHz. There was a clear difference when moving the Pioneer horn backwards, compensating for the different path lengths. In the usual setup, like a Belle K, and using pink noise as sound. The sound image from one loudspeaker was like coming from to distinct sources, the lower part and the upper part. Moving the Pioneer horn backwards the sound suddenly appered like one source, impossible to say that itcame from as specific part of the loudspeaker. The effect it had on the sound can most easily be described as reduced "harshness" to the music. Also the stereo image was much improved. This harshness is also described as "horn sound". I should also add that the x-over was the most simple, a first order, but it should be possible with any higher order Riley-Linkwitz x-over networks.
My question still remains, is there any experiments with lattice-networks or similar to compensate for the timing difference
?