I've done my fair share of solo drinking in Japan. I tend to bring Japanese manga or books with me and read at the bar. This is kind of a flag that says, "I speak Japanese". I've never failed to spend the evening chatting with people :-) So I don't think people are necessarily looking for solitude.
I also often see young women sitting by themselves in cafes. Sitting at a table by yourself sends a really different message. However, even then usually I find that regulars get to know the staff and that usually results in people getting to know each other. It's a bit like going to a local pub in the UK -- the staff introduces you to other people if you are a regular.
The absolute biggest thing that I find different is young women going on trips alone. This is incredibly popular and obviously a departure from older culture. My friends who were young when I met them (been here long enough that I don't have any young friends left!) often specifically wanted to travel alone. It was a kind of spirit of adventure. If you have only yourself to depend on, then it's more exciting. And they don't just go to safe places. I've had friends go camping in literal war zones! Maybe I just have crazy friends :-) For me, though, it's one of the biggest surprises of the current Japanese culture.
I've seen it quite a bit living here - airport buses especially tend to be crammed full of single women going to various places both within and outside of Japan. Coincidentally I've heard this used to explain why you see relatively few Japanese men dating foreigners.
Going out solo is great. That’s how you meet new friends. If you always hang out with the same group, you never expand your circle. I hope this whole culture of interdependency disappears.
I am reminded of the online quote by someone, “if you never learn to be alone, you will always be lonely.”