6" drivers absolutely can produce just as much bass as larger drivers if the speaker is designed/built for them. It's the
total air movement that counts. If TLSGuy disagree, he needs to provide some proof.
A few will, but you need massive motor systems and huge xmax. They are very expensive. Dyaudio drivers are no longer on DIY market, but some Morel drivers are the best example. However having more than one driver really helps as the VC heating is the square of the current X the VC resistance.
I have to say I try to avoid and listening to speakers with only one driver and that includes mids and bass drivers. That is why I chose to 10" drivers rather than one 15" driver with an Fs of 20 Hz.
In any event it is pretty obvious that as diameter goes down then stroke volume has to go up. That is true of all pistonic motion including internal combustion engines.
For speakers this makes the suspension much more complex as xmax increases. That also leads to higher Q drivers on the whole.
If you are going to get a lot of db from a small driver with low Q it means horn loading. That means a large speaker enclosure. That is the classic Lowther design.
If you have been thinking about designing speakers as long as I have you find out that you can not get the pint into a quart pot. If you try you have problems. In speakers the penalties are lowered output, reduced bass output, increased distortion, more thermal dynamic compression and higher F3.
If you look at the F3 of bookshelf speakers you are going to find F3 of the vast majority north of 50 Hz and an awful lot north of 60 Hz. But the real deal is reduced power handling without high distortion and thermal compression in the 80 to 600 Hz range especially.