Shouldn’t a true *sub*woofer extend below 20 hz?
I suppose... but subs that have usable low-distortion audio at 20Hz are RARE and expensive. Our ears aren't very sensitive at lowest frequencies so it takes lots of power, usually a big woofer, and a good design.
If you have small speakers you can get a LOT of additional bass by adding a sub that doesn't go all the way to 20Hz.
With a home theater system you (usually) don't get the "point one" channel at all without a separate subwoofer and it doesn't "need" to go to 20Hz either. If you have full-range speakers you can configure an AVR so the full-range goes to the main & surround speakers and only the "point one" LFE channel goes to the sub. And of course, that means pro studios DO need a sub for the LFE if they are mixing surround sound.
"Main" pro studio monitors will go down to 20Hz or lower and they may, or may not, include a subwoofer.
Pro subwoofers used live and in dance clubs are usually "tuned" to go down to around 40Hz. That's approximately the lowest note on a standard bass guitar and it's low-enough for bass you can feel in your body (if it's loud enough). There are usually compromises in speaker design and with certain trade-offs they can make a sub that's more efficient and louder if they don't go all they way down to 20Hz. It's the most logical way to fill a large venue with bass you can feel.
I'm not sure how common 20Hz bass is in movie theaters. I'm pretty sure that most theaters can't. The first Cerwin Vega "Earthquake" subwoofers used in the movie
Earthquake (in the 1970s) didn't go that low and they were just playing triggered-generated low-frequency noise because the film soundtrack format (optical?) didn't support low bass. The current model is spec'd at 36Hz.
I built a pair of 15-inch subs in large ported cabinets and I took a similar approach, tuning them to cut-off somewhere in the 30Hz range. I don't remember exactly but they can "rattle the walls" and annoy my nearby neighbors.

...So I don't really take advantage of them because i try to respect my neighbors.