I second John’s first sentence. Most music (except for pipe organ and such) does not go down to the last octave or two. But modern movies make a lot of use of that frequency range. So if you mostly listen to music, a pair of good speakers (especially ones designed for music) really won’t make much use of a sub.
Typical very good, but not audiophile speakers will be flat down to about the last octave (40hz) or even a bit lower (35hz–38hz). So for music and even for pretty good HT you will not miss a subwoofer.
Good subs are designed to be flat from 20hz or 25hz to about 80hz or 100hz., so in theory you will have paid for reproduction in the 40hz–80hz range (the second octave) twice.
However not all (even good) speakers are as flat in your room as the advertising brochures indicate. And crossovers typically are not binary in nature (at the crossover point), so even if your crossover is set at 80hz your main speakers are still being used to reproduce sounds perhaps as low as 60hz and your sub is being asked to reproduce sounds as high as 100hz.
This means that even if your main speakers are rated flat to 40hz (and this will be a pretty good speaker) they will still be being used at 60hz (assuming an 80hz crossover) and 60hz may well be about as low as your mains can reproduce accurately in reality in any case.
Which means that you have lost nothing and not paid for the same thing twice. But of course in the audio world, you have indeed been introduced to a prime example of the law of diminishing returns. That is, getting a thing to be a little bit better, costs a lot more.
