I think Boarderguy pretty much nailed it for me...1) I can dictate the pace of the dive without concern for my buddy's enjoyment as well.
2) If I get part way through a dive and don't feel it anymore I can go home without ruining the dive for my buddy
3) If I see something mid dive I can pursue it without concern or much thought about the "plan"
4) I can change my dive plan at any point in time based solely on my air. If I want to tool around at 30 ft after a deep dive I can or stay longer and run into deco.
5) No trying to sync my time to kit up with someone else. When I'm ready I splash.
6) I'm not trying to keep up with someone else.
My normal buddy and I normally splash together and follow a similar plan. We often get separated in our low vis water and continue the dive until it's time to surface (we have near the same SAC). That is how we do it and have zero concern for issues as we're fully redundant except his lack of a pony.
To add a bit...... up here in the PAC NW most of my cold water drysuit dives are hunting / gathering dives with limited vis end up being SOLO dives anyway so I want to be mentally, physically and equipped to be SOLO.
Also, as an instructor for 20 years (retired now)......I felt that most of my OW class dives were essentially SOLO anyway.
Plus, when diving warm water I am always rock'n my video system and focused on my subjects so I'm a lousy buddy if someone else needed me.
But the main reason I wanted the SDI SOLO cert is now that I'm 68 and still an active diver, my wife and I love our annual trip to Bonaire and she (also 68) is more into doing just one or maybe two dives a day max and I'm more into three to four.... So the SOLO cert allows me to be able to take the truck and go off on my own. Plus I love dusky and night dives on Bonaire and she does not. We always stay up in Sabadeco in a waterfront villa that's basically a 12 step staircase right down the the Andrea 2 site and SOLO gives me the option of just say'n..... "I'll be back in 90 minutes or less" and she can sit with a cocktail and watch my bubbles and or lights..
Last but not least.....I can think of no disadvantage of being 100 % trained and equipped to be self reliant even in a required buddy scenario (like in the Caymans where SOLO is prohibited. If my assigned buddy is either unwilling, unequipped or otherwise incapable of assisting me, then as a trained and equipped SOLO diver I am better able to survive.