"...and the 3dB difference enables the center to play twice as loud with the same power."
Doubling the power gives you a 3db increase in headroom, and a speaker with a 3db higher sensitivity would require half as much power to get to the same db, but to be "twice as loud" requires a 10db increase.
Further, if you combine the left and right speakers output that should result in a higher sensitivity. Combined, with identical signal and power to each, you would see a 3-6db increase depending on the speakers relative location to each other and the frequency. Assuming 3db is pretty safe, so in order for the center to have "twice the output of the left and right combined" the center would need 13 db more headroom, either in regards to sensitivity or through prodigal amounts of amplification. Assuming the voice coil could effectively take the amount of power it would need to gain 13db's (about 20 times the power/watts going to the left and right.
I see the point about the speaker maybe having the same sensitivity of the left and right combined, but I think you may have misstated in regards to the math and loudness.





