With the exception of perhaps a pipe organ note or two, there really aren't any traditional instruments that play deeper than the HT3's. So, for music, a sub is not really required and would not add much to the mix.
For home theater effects, that is a different story, especially for action type films.
But the problem is, to have really flat response to 20Hz, you really need to move a lot of air. That requires a very large subwoofer with a lot of power behind it.
We recently built a pair of large 15" subs that will be powered by 1000 watts each. The drivers alone were about 45 pounds. They would certainly do the job. But many smaller subs being marketed today are simply not capable of flat response to 20Hz without extensive EQ which robs you of power-handling. At those frequencies, it is all about moving a lot of air and that takes cone area and a lot of power, especially if you want to use a driver that can work well in a reasonably-sized cabinet.