Stereo as a consumer audio format dates back to the late 1950s with the introduction of the stereo LP, but monophonic LPs didn't fade all that quickly. They continued through the late 1960s for a few reasons, starting with the fact that monos were cheaper than stereo LPs, and some folks preferred the sound of monos. Retailers hated the "double inventory" requirements of carrying stereo and mono LPs of the same album, so monos quietly faded away.
That was nearly 50 years ago, but monophonic sound has returned in the form of Bluetooth speakers. While some BT speakers have built-in stereo drivers, they're so close together that the sound has virtually no separation, and winds up sounding like mono. Sure, a few folks buy pairs of BT and other wireless speakers, but most BT fans make do with one speaker. Home theater sound bars can indeed generate mild stereo separation, but it's never as good as a pair of speakers, placed 6 or more feet (1.8 meters) apart.
But mono's appeal isn't limited to the Bluetooth crowd; some audiophiles go out of their way to collect old mono LPs, which they prefer over stereo LPs of the same album. Most monophiles are jazz lovers, but there are legions of Beatles fans who much prefer the mono mixes of their albums. For the true believers among them the mono "Sgt. Pepper's" is the Holy Grail! They claim in the 1960s few UK Beatles fans owned stereo systems, so the Beatles focused most of their attention on mono mixes. I believe that's true, but I always heard the stereo LPs, and the monos seem drab and boring to me.
Just because you're listening to stereo recordings with stereo speakers doesn't guarantee you're hearing the music in stereo. Stereo can be "delicate": unless you sit in the middle, equidistant from the left and right speakers, you won't hear stereo as the mixers mixed it. So if you sit, for example, on the left side of your couch and you're 6 feet (1.8 meters) from the left speaker, but 9 feet (2.7 meters) from the right speaker, the stereo imaging will be completely out of whack. There are no ifs, ands or buts about it: You have to be the same distance from the left and right speakers to hear stereo properly. These placement issues are never a concern when listening over headphones -- with them you're always in the "sweet spot."
A great stereo recording listened to over a decent pair of speakers or headphones has an almost physical, three-dimensional presence. Take Radiohead's "Amnesiac"; the sound isn't merely strung out in a flat line between the left and right channels, there's spatial depth, and even an illusion of height. Some sound will appear forward of the speakers' locations. When playing music for an evening's entertainment the large and subtle shadings of depth and space from one recording to the next are endlessly fascinating.
With a really decent set of open-back, over-the-ear headphones the sound shouldn't be stuck inside your skull; music should sound like it's coming from just outside your head, from all around you.
If you have a "mono" button on your receiver or amplifier, try playing your favorite music first in stereo and then mono over speakers, and here's what you'll hear: In mono the sound constricts, space and depth shrink, dynamic contrasts suffer and the treble may dull. With headphones mono sound will be inside your noggin.
To answer my original question, "Is stereo sound twice as good as mono?" I think I was being too conservative. Stereo is a lot more than twice as good.