Jet,
We call that car with wire 22"s, two 18" subs and two bullet tweeters a Donk. And, we hear that hungover bass all the time.
That slooow bass has far less to do with the woofer size or individual woofer speed.
There are SPL woofers versus SQ woofers.
There are enclosures that are specifically designed to emphasize a single note and create more peak output...versus an enclosure alignment that is well-damped and intended to be linear (smooth response). You generally will not find pre-built SQ enclosures.
So system design and component selection plays a major role. System execution and tuning are major factors as well.
Its funny in that the Donk crowd is just as dissatisfied with a musical sounding subwoofer as you are with an indiscriminant sounding subwoofer.

David
Earmark Marine