Computer programs that accurately model the bass response of loudspeakers do not use cone diameter for anything other than calculating maximum SPL.
Exactly - that is where large woofers or several large woofers become important. And at low frequencies where hearing is much less sensitive it is generally obligatory to have very large woofer(s) in order to achieve SPL's greater than 100 db at 20Hz with minimal distortion. However, in a good design, with a high quality driver, a 6 inch woofer can do a pretty darn good job down to about 60 Hz - just don't expect miracles that defy the laws of physics. (Anyone with 6 inch woofers on their main speakers must have seen the remarkable excursions that they do when playing bass heavy music and these large excursions means that a fair portion of what you hear is distortion)