Center channels are very difficult and should be the most expensive speaker probably. For me they are a difficult challenge.
You want them relatively small and the driver as close as possible to the screen. The side MTM is a mess and I do not like it. So options are a three way with tweeter above mid, and side to side woofers with a low crossover. I don't like passive crossover below 400 Hz. I note B & W have upped their woofer to mid crossovers to 500 Hz. So to make a good job of a three way demands an active design or at least a hybrid. The other options are a coaxial driver or full range driver.
I opted for a coaxial solution with active BSC.
This gives good dispersion over the listening area with good dispersion to 60 degrees off axis +. So the listening area is well covered without exciting too much reflection.
That is my center response on axis and out to 60 degrees. I suspect the slightly lumpy response below 500 Hz is due to reflections from the screen. That is another problem with centers you have a hard reflective surface from the screen just where you don't want it.
One of the big issues is power handling. If you don't have a center, then the center dialog or singer is shared between two speakers. In a discrete multi channel recording then the center has to produce the entire spl. This of course places a big power load on the center speaker. I have had to replace one tweeter in my center, even though the crossover is 2.9 KHz and an electrical roll off of 18 db per octave.
The BBC have been doing some experimental multi channel broadcasts in the last 12 months. They do not have a center channel signal, just right left and surrounds. They are of the view that a center channel in the domestic environment is a detriment. I have to say they may well have a point
My observation of other rigs I listen to is the center integration is sub optimal far more often than not.