08-22-14: Timlub
Johnnyb53, are you saying that all 6.5 inch drivers start beaming at 2086hz....???
Actually no; it's not that simple. The significant measurement is the actual moving cone's diameter. A 6.5" driver with a large surround might have a 5" cone, but that would still beam at about 2700 Hz, somewhat shy of 3K. However, this can be offset by a 1st order slope for the tweeter crossover. If a tweeter crosses over at 3K at a 6dB/octave slope, then it's still putting out significant output at 1.5K, and would be down only 3dB at 2250Hz, which would be enough for good dispersion at the crossover point.
There are other ways to cheat the dispersion formula somewhat with phase plugs, waveguides, and whizzer cones. Still, I mentioned the formula with a link to the wavelength calculator to answer the OP's question--why have a small diameter midrange when a larger one would provide larger radiating surface? One answer is that the larger driver has the potential to create an in-room 1/2-octave wide suckout around the crossover point.
A better solution might be dual mids or dual or triple tweeters. Dual small mids would provide more radiating surface while maintaining small diameter diaphrams for better dispersion. Multiple tweeters would allow using a lower crossover point without overdriving the tweeter. This is what Tekton does in mating a 10" woofer with a 1.5" ring radiator. Some of the 10" woofers have whizzer cones with 3 tweeters instead of one on his top line models. This enables lowering the crossover point to let the tweeters cover for the woofer's beaming.
The worst case is a 2-way with a large woofer, small tweeter, and 4th order (24 dB/octave) crossover to increase power handling. It means the tweeter wouldn't be able to improve dispersion just below the crossover point because output would be too far down to help out.
Why do you think there are so many speaker manufacturers and DIYers? Dynamic speakers in boxes present balancing acts with an infinite number of possibilities in driver sizes, driver numbers, crossover points, crossover slopes, as well as cabinet size and bass alignment. Not to mention the actual individual driver characteristics.