How do I know if I need a sub woofer?

Maybe you haven’t heard a truly good system that delivers excellent imaging and soundstage without the aid of subwoofers.
 

@lanx0003  Well yes I’ve heard plenty of those systems, and it’s clear you’ve never heard good subs properly dialed in or you’d understand what I and several others here are saying, but clearly you do not.  Saying something ignorant like subs aren’t needed if your speakers go down to 30Hz just underscores you’ve no idea what you’re talking about here and what subs done right can actually do.  There’s a reason companies like Magico, Wilson, and others make subs costing into five figures, and it’s not just to pair with monitors.  Case in point, here’s a Stereophile review of the Wilson LōKē sub paired with the Alexia V that go down to 19Hz where the subs made a substantial improvement not only in the bass but in the overall soundstage.  Pretty much says it all and completely debunks your position. 

https://www.stereophile.com/content/wilson-loke-subwoofer

From the conclusion of the review…

I expected bass to be bigger, deeper, and more fleshed out with the LōKē. That it certainly was. What I did not expect was the ability of Wilson's smallest subwoofer to enhance every aspect of the listening experience—especially the sense of space. As the soundstage grew deeper, wider, and more coherent, as soundstage boundaries became more evident, as air between and around instruments and voices increased and the quality of music reproduction rose to mesmerizing levels, my appreciation for the transformative potential of the LōKē grew exponentially.

I am happy with the sound....enjoy listening to music...have an incredible fleshed out sound with delightful micro dynamics that make the music accessible. So why would I need a subwoofer? 

For all the reasons listed above.  It makes everything better when done right.  I bought two and it took my system to the next llevel, improving soundstage depth and width as well as imaging.  Of course it also filled in below where my stand mounts cut off.  I would not build another system without them.  

**Maybe you haven’t heard a truly good system that delivers excellent imaging and soundstage without the aid of subwoofers.

Well yes I’ve heard plenty of those systems...

Okay, you had. Then I am not concerned that you might be as ignorant as you were on the other subject like the cable impedance issue. So let me ask you if the soundstage is already ’excellent,’ why do you need an additional subwoofer to artificially expand it. What you experienced is likely the reverberation added by the subs, going beyond what the actual music content presents. Remember, my bullet #2 in the original statement already covers my requirement for soundstage.  Don’t just quote the bullet #1.

My system renders a soundstage wider than my speakers, which are set 11 ft apart, and deep enough that at times I feel like I could walk into it when such music content is in the recording. The height also resembles the actual performer’s presence. What more could one reasonably want from subs?

So let me ask you if the soundstage is already ’excellent,’ why do you need an additional subwoofer to artificially expand it. What you experienced is likely the reverberation added by the subs, going beyond what the actual music content presents.
 

@lanx0003  The sub is reproducing frequencies and information not previously presented by the speakers because they can’t.  That’s not artificial, it’s just uncovering more of the recorded information that’s already there.  If you think that’s artificial then you go ahead and believe that. 
 

What more could one reasonably want from subs?

Did you not read the review of the Wilson sub?  That’s what good subs properly set up can provide and perfectly coincides with what I’ve heard, and that’s in a system that likely makes yours look like a toy in comparison.  If you wanna just go on convincing yourself that your system is perfect and subs would provide no benefit and are artificially enhancing sound then live happily ever after in denial, but as I and many others here have heard for ourselves you’re not even aware of what you’re missing.  Ignorance is bliss.