I have asked that question myself over the years,
As a teenager, do I need a subwoofer for the car? Well, considering the limits of 6.5 inch speakers--you bet! Back in the dorm days, the same question of "need" popped up. I had a small pair of bookshelves that I loved the sound quality--it was perfect except for "rock star" (party) mode. Used a pair of 15 inch PA speakers to do high SPL party mode--all good? No, wanted the bass of the PA speakers so--I purchased my first subwoofer. Did the sub crawl to get it in the right spot--shock and awe--it was not in the same location of my bookshelves.
However, I finally was able to go down to 30Hz with the bookshelves and the die was cast. Years go by, I purchase a new pair of smalllish speakers with more SPL capability, more efficient and then went with a 25 Hz capable subwoofer. Pondered getting a second one to get better coverage since I was not single anymore so--purchased another sub and it was mo bettah!
My new speakers went down to 35 Hz before rolling off slowly (sealed speakers) but even when listening to music that did not have deep bass, they sounded better with subwoofers and it was obvious when several people were involved. For me, for the music I listen to and the fact that Youtube, TV programs, movies and video games on occasion get pipped through--subs work the best for me. However, I don't listen to bass shy records, only listen to AM radio rock etc. so if you do--the demand for subwoofers will be less. This does not mean you get the befefits of multiple subwoofers or to place the subs in the best location to get the most even bass response. If you live alone, have the chair to listen in a specific location you can go with one sub properly managed or even no sub depending on your room acoustics and use. That question is how important bass response is to you, how much bass and how low it goes in your music and so on. I can't answer for you.
Be aware that the subwoofer was invented in 1968 by Infinity so your question has been asked for over 50 years.
The correct answer is "that depends" but you might have noticed that from the unicorn of the late 60's to professional use in theaters in the 70's to car and audiophile use in the 80's then HT in the 1990's--they are not going away. The 2 channel receivers of yore are now a niche' product with the rise and domination of the AVR. When I purchased my first AVR it was to drive a "2.1" system which morphed to a 3.1 system then 3.2 to 5.2 and so on. It has been 30 years plus since I was a kid building ttwo 8" sealed subwoofers to solve my bass problem. The problems and acoustic issuez still exist be in car, boat, PA, HT or simple 2 channel. The first subwoofer system in a house that I was able to touch was a 2.2 system. The guy was in his late 30's and had a taste for classical music so two big M&K subwoofers was his solution (and EQ etc.)
I do find it odd that some people think that 2 channel means only 2 speakers. This would exclude subwoofers, bi/tri-amping and anything over the past 50 years to improve the stereo experience. Pro audio went mutli-channel systems decades ago even if it only "left/righ". Don't be afraid to use subwoofer os active crossovers and mutliple amplifiers if the juice is worth the squeeae. After all, when all the subwoofers and bi/tri/quad active systems started to make a move the record was still the top seller at the local music store , Sears or curcuit city. (remember them?) It is just a silly hobby, nobody "needs" 2 channel anymore than they "need" subs--mono works just fine! If you want better sound quality, more even bass response in your room, have multiple people listening to the music/moves etc. then subwoofers can and will help. I know they did for me--30 years ago by your mileage may vary. If you have friends that own subs, maybe you can pay them kickback money to "borrow" them for a weekend and play around with the things. If that won't happen, you can ask if you can learn and listen to how they system operates. I've taught dozens of people over the years how they work but generally won't let them take them home--I am cruel that way.
Most people just ask because it IS an investment so best to play around with a system by a person that knows how to do it properly first.
Another idea is to find an AVS get together--the DIY side tends to do that fairly often. They ALWAYS use subwoofers but also test various speaker designs without subwoofer support as a test. If you could attend one of the DIY get togethers, you might learn more about subs than you ever wanted to know. Be aware that you might then spend a ton of money and take over the living room with subs and large speakers--you have been warned!
It is hard to explain it with words, much easier to digest when you get to pay around with a system setup properly by a person that knows what they are doing. Just consider it a field trip but this time you can bring the beer and wings. That is what I would do if it was still a question in my mind.
Just remember, this is supposed to be fun and educational--jump right on in, the water is fine! Good luck.