Only infrequently do I dive truly 'solo' - i.e. I am the only one at the quarry, or in the water - not because of concerns about safety, but more as a matter of convenience. I often dive quarries in my drysuit, and I have a back-zip suit, which is hard to get into solo. If I am going wet, I am usually going for the social aspects of diving (especially the apres-dive snacks and beverages), or because we have a specific training mission, so having a buddy in the water makes functional sense. At times, though, I will dive the quarry wet, and solo, ahead of a weekend class for example, to either set up for the class (e.g. run a tape line for AOW kick cycle measurement) or check conditions (tempertaure and visibility) in advance.
I enjoy diving 'solo' on some ocean dives - I might take a group of divers on a new diver charter, and meander around on the wreck while the group of buddy pairs swim around and enjoy themselves, and then hang out on the wreck by myself for a few minutes after everyone else has ascended - it is amazing how much 'noise' there is in the water. Or, I might be the last one in the water and pull the anchor / tie in. But, for coastal charters I am usually in the water with a group of people, although the distance separating us is large enough that I would consider it functionally to be solo diving. I admit, though, that doing solo night dives in Bonaire is one of the most relaxing aspects of our group trips to the island.
There are some real advantages of having a buddy, as a second set of eyes. I was diving a wreck off the NC coast last week at 100', and my dive buddy spotted a huge sea turtle and signalled me to come take a look. My buddy was about 40 feet away from me when he spotted it, and I would have probably missed the turtle altogether had he not been in the water (and had I not happened to turn and look in his direction at the right moment). I then saw another diver who was probably 40 feet away from me, also by herself, and swam over and signalled her to come take a peek at the turtle.
But, my buddy and I also dove a wreck during the same 3 day trip, at 170', and he went down alone ahead of me (I had an issue with the reg on a deco bottle when I pressurized it, and had to quickly swap out the reg, but after he was geared up and ready to splash). He went down solo, I then went down solo, and we both swam around for ~15 minutes on a large (470') wreck before we hooked up near the tie in point, for the last 10 muinutes of bottom time. We then ascended, and did our deco stops, together.
The other advantage of diving with a group, even if there are no 'buddy' teams, is comparing notes on the dive afterward and, of course, telling stories on one another afterward.