Not sure the OP mentioned the room size he/she intends to use whatever speakers meet his/her four criteria.
I think the smaller the room, the more I would agree with kosst_amojan and rbstehno that you don't need giant woofers for great dynamics. Well designed smaller woofers in numbers are rather potent.
However, I think extremely large rooms or even outdoor venues where one is wanting to top 100+ decibel levels is where the point about physics and horn-loaded speakers as suggested by analogluvr and phusis becomes more prevalent.
For a modestly sized home room space, I don't think 15 inch woofers and large horns are needed to achieve what the OP desires. On the other hand, if you're wanting to fill an "auditorium" with sound, I think you would have to go with multiple 15 inch woofers and horns.