As full integration of subwoofers is quite difficult and because most subwoofers cannot keep up with many midrange drivers and tweeters, I would seek to avoid them. But because these same problems bedevil full range speaker designers, there is no easy advice to give.
For a long time I had Beauhorns with a single driver. They were great from about 65 Hz to 13k Hz. I finally found subwoofers and an amp that would keep up with them using a high pass filter on the subwoofer amp starting at 40 Hz and the natural roll-off of the Beauhorns. It looked good on instruments and was satisfying, but when I got the Acapella LaCampenellas, I realized that there was much missing from about 125 Hz to 50 Hz. But with the Acapellas I don't have house shaking frequencies below about 28 Hz.
So the answer to your question is both absolutely you need subwoofers and absolutely no subwoofers are impossible.
For a long time I had Beauhorns with a single driver. They were great from about 65 Hz to 13k Hz. I finally found subwoofers and an amp that would keep up with them using a high pass filter on the subwoofer amp starting at 40 Hz and the natural roll-off of the Beauhorns. It looked good on instruments and was satisfying, but when I got the Acapella LaCampenellas, I realized that there was much missing from about 125 Hz to 50 Hz. But with the Acapellas I don't have house shaking frequencies below about 28 Hz.
So the answer to your question is both absolutely you need subwoofers and absolutely no subwoofers are impossible.